* Saudi-led coalition welcomes Saleh's comments
* Rift widening between Saleh and his Houthi allies
* Fourth day of fighting between Saleh supporters, Houthis (Adds additional quotes)
ADEN, Dec 2 (Reuters) - Former Yemeni President Ali Abdullah Saleh said on Saturday he was ready for a "new page" in relations with the Saudi-led coalition fighting in Yemen if it stopped attacks on his country.
The call came as his supporters battled Houthi fighters for a fourth day in the capital Sanaa while both sides traded blame for a widening rift between allies that could affect the course of the civil war.
Together they have fought the Saudi-led coalition which intervened in Yemen in 2015 aiming to restore the internationally recognised government of President Abd-Rabbu Mansour Hadi after the Houthis forced him into exile.
The clashes between Saleh's supporters and the Houthis underscore the complex situation in Yemen, one of the poorest countries in the Middle East, where a proxy war between the Iran-aligned Houthis and the Saudi-backed Hadi has caused one of the worst humanitarian catastrophes in recent times.
"I call upon the brothers in neighbouring states and the alliance to stop their aggression, lift the siege, open the airports and allow food aid and the saving of the wounded and we will turn a new page by virtue of our neighbourliness," Saleh said in a televised speech.
"We will deal with them in a positive way and what happened to Yemen is enough," he added.
Saleh, who was forced to step down by a 2011 mass uprising against his 33 years in office, said Yemen's parliament, which is dominated by his GPC party, was the only legitimate power in the country and was ready for talks with the coalition.
The Saudi-led coalition welcomed Saleh's change of stance.
In a statement carried by the Saudi-owned Al-Hadath channel, the coalition said it was "confident of the will of the leaders and sons" of Saleh's General People's Congress (GPC) party to return to Arab fold.
The coalition accuses non-Arab Iran of trying to expand its influence into Arab countries, including Yemen, which shares a long border with Saudi Arabia, by aligning themselves with the Houthis and Saleh.
The Houthis accused Saleh of betrayal, and vowed to keep up the fight against the Saudi-led coalition.
"It is not strange or surprising that Saleh turns back on a partnership he never believed in," the group's political bureau said in a statement. "The priority has been and still is to confront the forces of aggression."
Residents of Sanaa described heavy fighting on the streets of Hadda, a southern residential district of the Yemeni capital where many of Saleh's relatives live, early on Saturday, with sounds of explosions and gunfire heard while the streets were deserted.
The fighting eased in the afternoon as Saleh supporters gained the upper hand, but intermittent gunfire was being heard.
There was no immediate word on casualties. Both sides have reported that at least 16 people were killed in the fighting, which began on Wednesday when armed Houthi fighters entered the main mosque complex, firing RPGs and grenades.
Saleh's GPC party accused the Houthis of failing to honour a truce and said in a statement on its website that the Houthis bear responsibility for dragging the country into a civil war.
It also called on supporters, including tribal fighters, to "defend themselves, their country, their revolution and their republic..."
The GPC appealed to the army and security forces to remain neutral in the conflict.
But the head of the Houthis' Ansarullah group warned that the biggest winner from what he described as Saleh's "sedition" was the Saudi-led coalition.
"I appeal to the leader Saleh to show more wisdom and maturity... and not to heed incitement calls," Abdel-Malek al-Houthi said in a speech on the group's Al-Masirah TV, adding that his group was ready to sit down for arbitration and abide by any ruling.
Yemen's civil war has killed more than 10,000 people since 2015, displaced more than two million people, caused a cholera outbreak infecting nearly one million people and put the country on the brink of famine. (Additional reporting by Omar Fahmy in Cairo; writing by Sami Aboudi; editing by Jason Neely)