CAIRO Oct 13 (Reuters) - Egyptian President Abdel Fattah al-Sisi denied on Thursday Ethiopian accusations that his country was supporting the opposition after a wave of violent protests that left hundreds dead.

Ethiopia accused "elements" in Eritrea, Egypt and elsewhere on Monday of being behind protests over land grabs and human rights that prompted the government to declare a state of emergency.

The unrest has cast a shadow over Ethiopia, where a state-led industrial drive has created one of Africa's fastest-growing economies, but whose government also faces criticism at home and abroad over its authoritarian approach.

Ethiopia's government spokesman said Egypt, which is embroiled in a row with Addis Ababa over sharing Nile waters, was a source of backing for armed gangs though that backing may not come from state actors.

Sisi denied those accusations.

"Egypt does not conspire against anyone," he said in a speech to the military.

"I want to assure the brothers in Ethiopia that Egypt has never ever offered any support to the opposition and will not carry out any conspiratorial action against Ethiopia."

The construction of Ethiopia's 6,000-megawatt Grand Renaissance Dam has become a bone of contention between Ethiopia and Egypt, which lies downstream and relies on the Nile River for agricultural, industrial and domestic water use. (Reporting by Ali Abdelatti, Writing Lin Noueihed; Editing by Hugh Lawson)