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. Violent clashes between rival factions in Yemen's rebel-held capital signal the disintegration of the rebel alliance at war with a Saudi-led coalition for almost three years.
"We will deal with them in a positive way and what happened to Yemen is enough", he added. The Houthi allied themselves with the forces loyal to Saleh and have fought a devastating war against forces loyal to Hadi and his foreign backers.
Citing the restricted access to his country, Saleh said Saturday in a televised address on Yemen Today TV that he is open to talks with the Saudi-led coalition. He said his offer would require Riyadh to stop attacks on Yemen.
Three Houthi leaders have so far been killed in the clashes that began on Friday, revealed the source, while noting that there have been more casualties among the militia ranks than among Saleh's forces.
Mr Hadi, in a statement after a meeting with his advisors, also said he was ready to work with Mr Saleh against the Houthis.
The Saudi-led coalition - which has fought Saleh and the Houthi rebels since 2015 - last month imposed a total blockade on the impoverished country after a rebel missile was shot down near Riyadh.More news: All Blacks Sevens beaten by South Africa in Dubai final
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In a televised address, Saleh called for new relations with the Saudi-led coalition, which he and the Houthis have been battling for nearly three years (since March 2015). "The priority has been and still is to confront the forces of aggression".
"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 United Nations envoy to Yemen, Ismail Ould Cheikh Ahmed, and the ICRC urged the parties to avoid targeting civilians.
He told Yemenis all across the country that if they support him, "to defend the nation, the republic and the revolution".
He also points up that Saleh's move represents a turning point in the situation inside the country, in which the tables have been turned against the Houthis, and the situation has returned to the status-quo prior to September 2014, when the Houthis seized chunks of the capital from former president Hadi.
Yemen's war has killed more than 10,000 people since 2015, displaced more than two million people, caused a cholera outbreak infecting almost one million people and led the country on the brink of starvation.