The rebel alliance controlling
The overture by former president Ali Abdullah Saleh follows a wave of deadly clashes between his supporters and Iran-backed Huthi rebels that has left dozens dead or wounded in Sanaa.
The former enemies joined ranks in 2014 to seize the capital and drive out Saudi-backed President Abedrabbo Mansour Hadi, whose government has taken refuge in the country's south.
But their fragile alliance has shown signs of unravelling for months and talks between them on Friday failed to broker a truce.
Saleh said Saturday that he was ready to talk to the Saudi-led coalition if it lifts a crippling blockade imposed on the impoverished country last month after a rebel missile was shot down near Riyadh.
"I call on our brothers in neighbouring countries... to stop their aggression and lift the blockade... and we will turn the page," he said in a televised speech.
"We vow to our brothers and neighbours that, after a ceasefire is in place and the blockade is lifted ... we will hold dialogue directly through the legitimate authority represented by our parliament."
Rebels denounce 'coup'
The Huthis quickly hit back, accusing Saleh of staging a "coup against our alliance".
His speech had "exposed the deception of those who claim to stand against aggression," a Huthi spokesman said in a statement carried by the rebels' Al Masirah TV.
The Yemen war has claimed more than 8,750 lives since Saudi Arabia and its allies joined the Hadi government's fight against the rebels in 2015, triggering what the United Nations has described as the world's worst humanitarian crisis.
Nearly one million people have been infected by cholera in Yemen this year, including more than 2,200 people who have died, according to the World Health Organization.
Saleh loyalists and rebel fighters continued to clash on Saturday afternoon in Sanaa, where violence has left at least 40 fighters dead or wounded since Wednesday according to rebel chief Abdulmalik al-Huthi.
Saleh has accused the Huthis of seeking to monopolise power and the rebels have accused the strongman of treason over his suspected contacts with Saudi Arabia.
The Saudi-led coalition on Saturday welcomed Saleh's offer of talks, a move the Huthi-run Al Masirah TV said showed the coalition's "faith" that the former president would reverse alliances.
"The decision by (Saleh's) General People's Congress to take the lead and their choice to side with their people will free Yemen of ... militias loyal to Iran," the coalition said in a statement carried by the official Saudi Press Agency.
Saudi Arabia and the United States have accused Iran of supplying weapons to the Huthis, which Tehran strongly denies.