The call came as his supporters battled Houthi fighters for a fourth day in the capital Sanaa as the two sides traded blame for a 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.
Yemen strongman Saleh open to negotiations with Saudi Arabia
The clash between Saleh's supporters and the Houthis underscores 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 stepped down after 33 years in office in 2012, following months of Arab Spring protests against his rule, but remained leader of the GPC, the country's largest political party.
Yemen's Huthi rebels fear 'coup': Saleh
The Saudi-led coalition welcomed Saleh's remarks. 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 says Saleh betrayed Arabs by joining Houthi-led forces who they say are aligned with non-Arab Iran.
Saleh controls southern Sanaa
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, including his nephew Tareq, live, early on Saturday, with sounds of explosions and gunfire heard all over the area.
The fighting subsided by the afternoon as Saleh supporters secured control. There was no immediate word on casualties.
Saleh's GPC party accused the Houthis of failing to honour the truce and said in a statement on its website that the Houthis bear responsibility for dragging the country into a civil war.
Turkey freezes assets of Yemeni ex-president Saleh
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.
The fighting began on Wednesday when Saleh's GPC party accused the Houthis of breaking into the city's main mosque complex and firing RPGs and grenades.
Both sides reported that at least 16 people have been killed in the fighting since Wednesday.
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.
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