SANA, Yemen — For decades, Mustafa Elaghil’s family produced snack foods popular in Yemen, chips and corn curls in bright packaging decorated with the image of Ernie from “Sesame Street.”

But over the summer, a military coalition led by Saudi Arabia sent warplanes over Yemen and bombed the Elaghils’ factory. The explosion destroyed it, setting it ablaze and trapping the workers inside.

The attack killed 10 employees and wiped out a business that had employed dozens of families.

“It was everything for us,” Mr. Elaghil said.

The Saudi-led coalition has bombed Yemen for the last 19 months, trying to oust a rebel group aligned with Iran that took control of the capital, Sana, in 2014. The Saudis want to restore the country’s exiled president, Abdu Rabbu Mansour Hadi, who led an internationally recognized government more aligned with its interests.

But instead of defeating the rebels, the campaign has sunk into a grinding stalemate, systematically obliterating Yemen’s already bare-bones economy. The coalition has destroyed a wide variety of civilian targets that critics say have no clear link to the rebels.

It has hit hospitals and schools. It has destroyed bridges, power stations, poultry farms, a key seaport and factories that produce yogurt, tea, tissues, ceramics, Coca-Cola and potato chips. It has bombed weddings and a funeral.

The bombing campaign has exacerbated a humanitarian crisis in the Arab world’s poorest country, where cholera is spreading, millions of people are struggling to get enough food, and malnourished babies are overwhelming hospitals, according to the United Nations. Millions have been forced from their homes, and since August, the government has been unable to pay the salaries of most of the 1.2 million civil servants.

Publicly, the United States has kept its distance from the war, but its decades-old alliance with Saudi Arabia, underpinned by tens of billions of dollars in weapons sales, has left American fingerprints on the air campaign.

Many strikes are carried out by pilots trained by the United States, who fly American-made jets that are refueled in the air by American planes. And Yemenis often find the remains of American-made munitions, as they did in the ruins after a strike that killed more than 100 mourners at a funeral last month.

Graffiti on walls across Sana reads: “America is killing the Yemeni people.”

President-elect Donald J. Trump has not said whether he will continue United States support for the war, but has been very critical of Saudi Arabia, saying it does not “survive without us.” At a rally in January, he said Iran was “going into Yemen” and was “going to have everything” in the region, but he did not clarify how he would respond.

The sweeping destruction of civilian infrastructure has led analysts and aid workers to conclude that hitting Yemen’s economy is part of the coalition’s strategy.

“The economic dimension of this war has become a tactic,” said Jamie McGoldrick, the United Nations’ humanitarian coordinator for Yemen. “It is all consistent — the port, the bridges, the factories. They are getting destroyed, and it is to put pressure on the politics.”

In a written response to questions, a coalition spokesman, Maj. Gen. Ahmed Asseri, said the air campaign had halted the rebels’ advance, destroyed 90 percent of their rockets and aircraft and pressured them to join talks aimed at ending the war. He denied that the coalition sought to inflict suffering on civilians and said only facilities connected to the war effort had been hit.

He blamed the rebel group, the Houthis, for the humanitarian crisis.

“This is primarily the responsibility of the rebels, who have displaced Yemen’s legitimate government and who are impeding the flow of humanitarian supplies,” General Asseri said.

Saudi Arabia and other Persian Gulf countries are also among the top donors of aid to Yemen. So even as they undermine its self-sufficiency, they help sustain the population.

The air campaign’s civilian toll has led to calls by some American lawmakers to postpone arms sales to Saudi Arabia.

“It is a significant moral outrage that we continue to provide arms to Saudi Arabia and to participate in military operations in Yemen,” said Representative Ted Lieu, a Democrat from California who was a military prosecutor in the Air Force. “The United States is at risk of aiding and abetting war crimes in Yemen.”

A Country in Chaos

The difficulty in just getting to Yemen demonstrates how much the war has upended the country.

The internationally recognized government is based in Saudi Arabia and in the south of Yemen. For a recent 10-day trip to Sana and surrounding areas, a photographer and I had to obtain visas from the Houthis.

We could not book flights into Sana because the Saudi-led coalition had halted all commercial air traffic. The United Nations allowed us onto an aid flight. As soon as we touched down, we saw traces of the war: the scattered carcasses of destroyed airplanes along the runway.

Once in Yemen, we were told that we could not go anywhere without a representative of the Houthis. He was with us whenever we left the hotel. We did not visit military sites, which the coalition has heavily bombed to destroy the ballistic missiles that the rebels have fired into the kingdom, killing civilians.

But the damage and suffering caused by the war were everywhere.

Beggars displaced by the fighting thronged our car, pleading for money and food. Buildings destroyed by airstrikes dotted the capital: the Defense and Interior Ministries, the army and central security headquarters, the Police Academy and Officers’ Club, the Sana Chamber of Commerce and Industry, the homes of officials who had joined the rebels.

The conflict has split the country, with forces backed by gulf nations and nominally loyal to the exiled president in the south and east, where Al Qaeda and the Islamic State have staged deadly attacks.

But in the areas we visited in Yemen’s northwest, the rebels were firmly in control, their gunmen running checkpoints alongside police officers who had joined them. In Sana’s Old City, posters of “martyrs” killed in the war covered entire buildings. Trucks with mounted machine guns, carrying fighters, occasionally sped by.

Spray-painted across the city was the Houthis’ rallying cry: “God is great. Death to America. Death to Israel. Curse on the Jews. Victory for Islam.”

On the edge of town, Yemeni families snapped photos of the ruins of a reception center that the coalition hit with two airstrikes in a single attack last month while the Houthi-allied interior minister was receiving condolences for his deceased father. Human Rights Watch called the attack on the funeral “an apparent war crime.”

United Nations officials gave us photos of remnants found at the site that indicated it had been hit with at least one American-made, 500-pound, laser-guided bomb. American warplanes routinely use that class of bomb, and the United States has provided such bombs to the Saudi military.

‘What’s Missing? Everything!’

On an expanse of rocky ground near the town of Khamer northwest of the capital, where they have been since fleeing their homes last year, hundreds of families have built shelters out of canvas, plastic sheeting and mud bricks. Most survive on charity, eating rice and bread cooked on mud stoves fired with wood or garbage.

In one tent, Farea Gayid, 55, said he had worked as an army engineer until his unit collapsed when the airstrikes began. An attack near his home killed his neighbors, so he and his family fled on foot. A trucker gave them a ride to Khamer, so they settled there, joining the more than 2.5 million Yemenis who the United Nations says are internally displaced.

In August, the government could no longer afford to pay Mr. Gayid his $200 monthly salary.

“Now my children beg in the market,” he said. “If the situation continues like this, there is no future.”

While the war spawned Yemen’s humanitarian crisis, aid workers say coalition bombings of critical infrastructure have exacerbated it.

Before the war, Yemen imported 90 percent of its food, mostly through the Red Sea port of Hodeida.

Last year, the coalition bombed the port, damaging its cranes. Now ships often wait for weeks at sea to unload, and some goods are close to expiration by the time they arrive, said Mr. McGoldrick, the United Nations official.

The coalition has also bombed key bridges, including the main one between the port and the capital, forcing truckers to take long detours.

“It is an all-encompassing, applied economic suppression and strangulation that is causing everyone here to feel it,” Mr. McGoldrick said. “The collapse of the economy is starting to bite very hard.”

According to the World Food Program, 14.4 million of Yemen’s 26 million people do not have enough food, and malnutrition is rising.

The suffering is clear in the capital.

“What’s missing? Everything!” said Manal al-Ariqi, a doctor in Sana’s main pediatric hospital. “We lack medical staff, nurses and medicine.”

Upstairs, nearly every room contained a malnourished baby. Most had been born to mothers who had fled the war and were too disturbed or malnourished to breast-feed normally, said Ali al-Faqih, a nurse.

In one room lay 7-month-old twin girls, Ruqaya and Suqaina, both with sunken cheeks.

“We lost everything because of the war,” their grandmother Shariya al-Awaj said when asked why the girls were so small. “All we brought with us were our clothes.”

The Economic Wreckage

The destruction in Yemen could cripple its economy long into the future, and it is unclear how the country will rebuild.

“They have hit many factories on the basis of suspicion, but we never get the real reasons,” said Abdul-Hakeem Al Manj, a lawyer at the Sana Chamber of Commerce and Industry who is helping businesses document the strikes with an eye toward future prosecution. “Any institution that has a big hangar, they hit it directly.”

Some businesses said they suspected they were targets only because they continued to operate after the Houthi takeover.

“For Saudi Arabia, we are all Houthis,” said Haroon al-Sadi of the state-owned Amran Cement Factory, which once employed 1,500 people before it was bombed twice.

Plant workers showed us the remains of munitions they had collected, including pieces of at least one CBU-105, a cluster bomb unit that contains 10 high-explosive submunitions. They are manufactured by Textron Defense Systems of Rhode Island.

General Asseri, the coalition spokesman, said it had “no interest in damaging any aspect of the Yemeni economy,” and had made great efforts to avoid harming civilians. He declined to provide details about specific sites, but said the coalition had “accurate intelligence” that the sites we visited were “being used by militias to store weapons and ammunition or a command-and-control center.”

The war has left nothing untouched for the Alsonidar brothers, Khalid and Abdullah, who own a group of factories outside Sana.

The family works with an Italian company, Caprari, to produce agricultural water pumps. It also owns a brick factory, which was out of use, and was preparing to open a factory to produce metal pipes to go with the pumps, also with an Italian partner.

Twice in September, the compound was bombed, destroying all three factories.

Saudi news reports said the factories had produced rockets for the rebels, a charge the brothers denied. They and their Italian partners have written to the United Nations to state that the factories could not produce military technology, and to call for an investigation, which is continuing, they said.

“We’re not talking about something useless,” Abdullah Alsonidar said. “We’re talking about infrastructure and people’s lives. Strikes like this can bring a family to the ground.”

Remains of munitions that the brothers found at the site indicate that it was hit with American-made weapons, including one with laser-guidance equipment that was made in October 2015.