Forces loyal to Yemen's former President Ali Abdullah Saleh have denied claims by Houthi rebels who say they have gained control of most of the country's capital, Sanaa, according to an official in Saleh's Republican Guard.

Iranian-backed Houthi fighters say they had regained control of three military bases, the diplomatic district and other neighbourhoods around the area. They also said they had taken over the city of Dhamar, south of Sanaa, as well as its surrounding regions.

Sanaa has been shaken by escalating violence between Saleh's supporters and Houthi rebels. At least 40 people have reportedly been killed since Wednesday amid ongoing fighting between the two sides, with residents now fearing a new front in an already devastating war.

Though clashes subsided on Saturday night, residents in Sanaa told local media outlets that fighting resumed on Sunday.

According to reports, clashes erupted in some neighbourhoods in the heart of the Yemeni capital.

Residents reported hearing sounds of explosions in Hasba, while others said coalition airstrikes struck Houthi targets south of the city. 

On Saturday, Saleh said that he was open to talks with a Saudi-led coalition fighting Houthi rebels, in what the fighters called "a coup" against their fragile alliance with the former president.

He also called for a joint ceasefire between his supporters and Houthi rebels, and the Saudi-led coalition, which has been bombing the impoverished country since March 2015 to get rid of the Iranian-backed rebels.

The Saudi-led coalition praised Saleh for "taking the lead" in the conflict. In a statement on Saturday, the coalition said that it would "redeem Yemen from the evils of Iranian terrorist and sectarian militias, return it to the Pan-Arab pure and natural fold".

Ibrahim Qatabi, Doha-based political analyst, told Al Jazeera: "It seems to me that there might be some collaboration between regional powers, Saleh and maybe the legitimate government to somehow overthrow the Houthis first and then have a serious political talk."

"This is what it looks like, where the whole thing is headed," he said.

Saudi Arabia along with other Sunni Muslim countries intervened to reinstate the government of President Abd-Rabbu Mansour Hadi, who was overthrown by the Houthis in 2014.

In May 2015, following Saudi-led coalition air raids on his home in Sanaa, Saleh officially announced for the first time the establishment of his alliance with the Houthis. A year later, the Saleh's General People's Congress (GPC) party and Ansar Allah, the political arm of the Houthis, signed an agreement to form a political council to run the country.

The Saudi-led coalition imposed a total blockade in October on the country, where nearly 80 percent of the people need humanitarian aid to survive.

Last week, amid mounting international pressure over the suffering of millions of Yemenis, some humanitarian aid was allowed to enter the country.

The war in Yemen is one of the worst humanitarian crises in the world, killing at least 10,000 people and leading to widespread hunger and disease.