Ali Abdullah Saleh, Yemen's former president and longtime strongman who ruled the country for over three decades, was killed on Monday, according to multiple Yemeni officials, as his loyalists and Houthi rebels battled for control of the capital.

Circumstances of his death remained unclear but some officials claimed that the rebels killed him as he tried to leave the capital.

The Houthi-run Masirah TV announced the death of the “leader of the traitors” on Monday, referring to Saleh, who until last week was in a fragile alliance with the rebels.

A statement read on the channel announced the “end of the crisis of militias”, referring to Saleh's armed supporters, and “the killing of their leader and a number of his criminal supporters”.

A senior official with Yemen's internationally-recognised government confirmed to The Associated Press that Saleh had been killed. He sent a video purportedly showing Saleh's body being carried away by a group of armed men chanting, “God is Great.”

The official spoke on condition of anonymity because he wasn't authorised to speak to the press. It was not immediately possible to confirm the authenticity of the video, which was circulating widely.

Two of Saleh's associates have also confirmed, along with a third official from the government of Yemen's internationally recognised president, Abd Rabbu Mansour Hadi.

An AFP photographer who approached Saleh's home in southern Sanaa on Monday found it in the hands of the Houthis and was prevented from entering. The house appeared to have been damaged in fighting.

Gun battles forced shops and schools to close in Yemen’s capital Sanaa on Sunday as residents warned a three-year rebel alliance was collapsing into a “street war”.

The Houthi rebels’ partnership with the powerful ex-president appeared to have fallen apart after he reached out to a Saudi-led coalition fighting the insurgents.

The Houthis’ political office on Saturday accused Saleh of staging a “coup” against “an alliance he never believed in”.

Heavy fighting in Sanaa

As witnesses reported continued heavy fighting on Monday, President Abedrabbo Mansour Hadi ordered his forces to launch an offensive to advance on the capital.

“The president has ordered Vice President Ali Mohsen al-Ahmar, who is in Marib (east of Sanaa), to activate military units and advance towards the capital,” a presidency official told AFP, speaking on condition of anonymity.

The government also reached out to Saleh's supporters with an offer of amnesty.

“The president will soon announce a general amnesty for all those who collaborated with the Houthis in recent months and who have retracted that allegiance,” Prime Minister Ahmad Obaid bin Daghr said.

The Saleh-Houthi alliance had been fraught since its inception in 2014, when the two ended decades of enmity and joined ranks to capture Sanaa from Hadi's government.

Saudi Arabia, accusing arch-rival Iran of backing the rebels, intervened in the Yemen war on behalf of the government the following year. Iran has denied the accusations.

The Saudi-led coalition has been hitting Sanaa with air strikes for months, and a fresh wave on Monday targeted areas near Sanaa International Airport and the interior ministry, both under Houthi control, residents and an airport source said.

The coalition on Monday warned Yemeni civilians to avoid rebel areas.

“The coalition urges civilians to evacuate areas near positions held by the Houthis,” read a statement published by Saudi Arabia's state-run Al-Ekhbariya TV. “We ask civilians to remain at least 500 metres away from Houthi military vehicles and gatherings.”

Residents near the airport said multiple air raids had shaken their homes late on Sunday night and early Monday.

Fears for civilians

An airport source said rebel bases near the location appeared to have been targeted, but the airport itself had not been bombed.

Residents reported that the fighting, which erupted Wednesday, had spread outside the capital.

Tribal sources in Saleh's hometown Sanhan, south of Sanaa, on Monday reported intense overnight fighting between the Houthis and Saleh loyalists.

Witnesses said clashes had erupted around the residence of Tarek Saleh, a nephew of the former president and a leader with his forces.

Saleh on Saturday announced he was open to talks with Saudi Arabia and its allies on condition they ended their crippling blockade of Yemen's ports and airports.

That dealt a serious blow to his already fragile alliance with rebel chief Abdul Malik al-Houthi.

The Saleh-Houthi split sparked fears of a new front in the Yemen war, which has already claimed more than 8,750 lives since the Saudi-led coalition intervened.

The conflict has pushed Yemen to the brink of mass starvation and triggered what the United Nations has called the world's worst humanitarian crisis.

International aid groups warned on Monday they were losing the ability to reach civilians in Sanaa.

“Ambulances and medical teams can't access injured, people can't buy food and other supplies,” UNICEF's Rajat Madhok said on Twitter.

“Aid workers can't travel and implement critical life-saving programmes. This latest violence couldn't come at a worse time.”

Saleh ruled Yemen for more than three decades until he was forced to resign following an Arab Spring uprising in 2011. He remained in the country, however, and continued to wield power from behind the scenes.

In 2014, his forces allied with the Houthis despite the fact that as president he had gone to war with them on more than one occasion.

The rebel alliance splintered last week, setting off heavy clashes between the Houthis and Saleh's forces.