SANAA -  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 Iran-backed Huthi rebels' partnership with powerful ex-president Ali Abdullah Saleh appeared to have fallen apart after he reached out to a Saudi-led coalition fighting the insurgents. The Huthis' political office on Saturday accused Saleh of staging a "coup" against "an alliance he never believed in".

On Sunday, Saleh loyalists cut off a number of streets in central Sanaa and deployed heavily in anticipation of Huthi attacks, as security sources said clashes this week had left some 60 dead across the capital and at its international airport.

Saleh loyalists renewed a bid to seize control of Al-Jarraf district, a stronghold of the Iran-backed Huthis, who fortified their positions with dozens of vehicles mounted with machineguns, witnesses said.

They said the Huthis had brought reinforcements from their northern strongholds and deployed them in the south of the capital. The Huthis seized the home of rebel interior minister Mohammed Abdullah al-Waqsi, who is close to Saleh, killing three of his bodyguards and detaining others, Saleh sources said.

And Huthi rebels killed Mohammed al-Zarka, a tribal leader close to Saleh, in Omran just north of the capital and members of his family, the same sources said.

Sanaa residents said they had barricaded themselves in their homes to avoid snipers and shelling as clashes flared up around key ministries where the two sides had been working together just days before.

The education ministry cancelled classes Sunday, normally the start of the school week, and witnesses said some bodies of those killed in previous clashes this week were still lying in the streets. Iyad al-Othmani, 33, said he had not left his house for three days because of the clashes.

Mohammed Abdullah, a private sector employee, said his street had been cut off by militiamen and he was staying home to avoid checkpoints.

"Sanaa is becoming like a ghost town. There is a street war and people are holed up in their houses," said an activist who works with the International Organisation for Migration in Sanaa. "If the confrontation continues, many families will be cut off" and stranded in their homes, he warned.

Three years after they joined forces to drive the government of President Abedrabbo Mansour Hadi from Sanaa, the collapse of the Huthi-Saleh alliance is a key shift in Yemen 's complex war. Saleh ruled Yemen as president for 33 years after the 1990 unification of north and south Yemen .

A longtime ally of Saudi Arabia, he waged six separate wars against the Huthis, Zaidi Shiites who hail from northern Yemen . Saleh resigned under popular and political pressure in 2012, ceding power to his then-vice president Hadi, who now lives in exile in Saudi Arabia.

In 2014, Saleh announced he had joined forces with the Iran-backed Huthis, seizing the capital and setting up a parallel government as Hadi's administration fled Sanaa. That triggered a Saudi-led Arab force to intervene to prop up Hadi's government, an escalation in a war that has since killed more than 8,750 people and dragged the country towards what the United Nations calls the world's worst humanitarian crisis.

On Saturday, Saleh reached out to the Saudi-led coalition, offering to "turn the page" if it lifts a crippling blockade on the country. The Huthis accused him of treason.

Yemen 's conflict has been a key focus of tensions between Sunni-ruled Saudi Arabia and Iran, the predominant Shiite power.

The Saudi-led coalition carried out dawn air raids Sunday against Huthi positions in the hills south of Sanaa but it was unclear if the strikes were meant to benefit Saleh's forces.

A coalition spokesman could not immediately be reached for comment. The United Arab Emirates, which is a key member of the coalition, on Sunday denied a Huthi claim that a missile fired from Yemen reached its air space or threatened a nuclear power plant set to open in 2018.

The Huthis had earlier claimed on their Al-Masirah news channel that they had hit the Barakah plant with a cruise missile fired from Yemen . A missile fired by the Huthis which was intercepted by near Riyadh's international airport last month prompted the coalition to tighten a blockade against Sanaa airport and rebel-held sea ports.

The Huthis have warned that Saudi Arabia and its allies will "pay a heavy price in their own capitals" for Saleh's "great treason".