He says a new page must be opened in relations (with Saudi Arabia) and neighborly ties restored, putting an end to all (the animosity) that has taken place and that amicable relations can resume once there is a cease-fire (with the Saudi-led coalition) and their blockade of Yemeni ports and airports is lifted.
"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 statement carried by the official Saudi Press Agency said.
The Houthis are backed by Iran but have been Mr Saleh's allies against the internationally-recognised government of President Abdrabbuh Mansour Hadi since 2014.
Pointing to worldwide law, Lowcock said, "Wars have rules, and they need to be complied with".
Saleh was forced to surrender his office in 2012 amid a wave of mass protests in the country, abandoning the presidency to his Vice-President Hadi. He said his offer would require Riyadh to stop attacks on Yemen.
The Saudi-led coalition welcomed Mr Saleh's change of stance.
The Houthi chief also accused Saleh of secret collaboration with the leaders of the coalition.
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He urged the "turning a new page with all the political sides. and to form a broad national coalition that will lay the foundations for a new era and unify everyone against the coup militia".
The Houthi rebels denounced what they described as "sedition", meaning Saleh's behaviour towards the Saudi coalition. 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. "The priority has been and still is to confront the forces of aggression".
In response to Saleh's speech, Houthi leader Abdel-Malek al-Houthi stressed the need for dialogue in another televised appearance in Saturday, and called on Saleh to "be more mature".
He told Yemenis all across the country that if they support him, "to defend the nation, the republic and the revolution".
Saleh agreed to leave presidency in 2012, n 33 years in front of Yemen, after months of popular protests and global pressure (including that of its neighbours) to prevent anor civil war being unleashed as in Libya or Syria.
The GPC appealed to the army and security forces to remain neutral in the conflict.
"It needs to be fully wound down if we are to avoid an atrocious humanitarian tragedy involving the loss of millions of lives, the like of which the world has not seen for many decades", UN Undersecretary for Humanitarian Affairs Mark Lowcock said Friday addressing reporters in Geneva.