The coalition has also been accused of committing war crimes through indiscriminate attacks on residential areas in cities controlled by the rebel forces.
The rift between Saleh and the Huthis goes back months, with the former president slamming the Huthis as "militias" and the rebels threatening Saleh loyalists after armed violence left two dead in Sanaa in August.
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.
Former Yemeni President Ali Abdullah Saleh - whose supporters are now in a shaky alliance with the Houthi rebels in the fight against the Saudi-led coalition - tossed an olive branch on Saturday to Riyadh, saying he is open to talks with the coalition and ready to "turn the page".
"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".
"We will deal with them in a positive way and what happened to Yemen is enough", he added. The infighting threatens to unravel the fragile rebel alliance that controls the capital and has been battling the Saudi-backed government of President Abedrabbo Mansour Hadi in Yemen's war.
There was no immediate word on casualties. In a televised interview, Salah also called for resuming relations with Saudi Arabia, if the Saudi-led coalition lifts its blockade of Yemeni ports and air facilities.More news: Nigeria eye shock win after Argentina SWC draw
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The Saudi-led coalition welcomed Mr Saleh's change of stance.
"The uprising in Yemen's capital Sanaa is the sign of an awakening of the nightmare", UAE's Minister of State for Foreign Affairs Anwar Gargash said on Twitter. Saleh has accused the Houthis of seeking to monopolise power and the rebels have accused the strongman of treason over his suspected contacts with Saudi Arabia.
He told Yemenis all across the country that if they support him, "to defend the nation, the republic and the revolution".
The coalition accuses Saleh, who heads the General People's Congress party, of betraying his Arab neighbors by joining forces with the Houthi rebels.
"The GPC appealed to the army and security forces to remain neutral in the conflict".
"It demands the anti-government forces in Yemen to desist from attacks against the Kingdom of Saudi Arabia", the FO added.