Former Yemeni president Ali Abdullah Saleh says he is open to talks with the Saudi-led coalition fighting on behalf of the internationally-recognised government as fierce clashes continued for a fourth day in Sanaa between fighters loyal to him and Houthi rebels.

Mr Saleh and his supporters formed an alliance with the Shiite Houthis against the Yemeni government in 2014. But in recent months tensions have increased between the two sides.

Things came to a head earlier this week with fighting breaking out between the two sides on the streets of the rebel-held capital, with an official telling The National on Saturday that Saleh loyalists were now in control of most of the city.

"I call on our brothers in neighbouring countries … to stop their aggression and lift the blockade … and we will turn the page," Mr Saleh said in a televised speech on Saturday, according to Agence France-Presse.

The Saudi-led coalition has fought Saleh loyalists and the Iran-backed Houthis rebels on behalf of the government of president Abdrabu Mansur Hadi since March 2015. It closed Yemen's borders and shut access to its sea and air ports on November 6 in response to a missile attack launched by the Houthis that targeted Riyadh's international airport.

The Houthis slammed Mr Saleh's speech later on Saturday.

"Saleh's speech is a coup against our alliance and partnership … and exposed the deception of those who claim to stand against aggression," a Houthi spokesman said in a statement carried by the rebels' Al Masirah TV.

It came as a source in Sanaa told The National that residents were beginning to flee their homes on Saturday amid "fierce confrontations" between forces loyal to Mr Saleh and Houthi rebels.

The two sides were using heavy weaponry, including mortars, rocket-propelled grenades (RPGs) and anti-aircraft cannons, the source said.

A senior official in the rebel-run moral guidance department said elite renegade soldiers loyal to Mr Saleh had made major advances against the Houthis, seizing key rebel positions in the city and surrounding areas at rapid speed.

"Republican Guard forces control Sanaa airport, Al Sawad (military) camp, the ministry of finance, and the television area" in addition to the moral guidance department, the official told The National.

Most of the capital was now controlled by either Republican Guard forces or tribesmen loyal to Mr Saleh, the official said, adding that Saleh loyalists north of Sanaa were preventing any Houthi reinforcements from entering the city from the rebels' northern stronghold of Saada.

The official said Mr Saleh had called on his forces to return to their headquarters to keep the city safe, however, though political analysts expected the city to fall completely to his loyalists within hours.