The Saudi-led coalition had been fighting both the Shiite Houthi rebels and Saleh's party in Yemen since March 2015 to support the internationally-recognized government led by President Abd-Rabbu Mansour Hadi.
He fought six wars against the Houthis when he was president, but joined forces with them to take over the capital in 2014.
"We will deal with them in a positive way and what happened to Yemen is enough", he added.
A coalition statement said the decision to "take the lead and to side with their people will free Yemen of. militias loyal to Iran". 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.
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).
MEE tried to contact Houthi sources for comment on the fighting, but they declined to speak.Some Houthi supporters reported news via social media that Houthi fighters still control most of Sana'a.
On Thursday, Houthi threatened to retaliate again over a blockade imposed by the coalition, after a November 4 rebel missile attack that was intercepted near Riyadh worldwide airport.
However, the Houthis were less open to Mr Saleh's idea.
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The missile attacks, which could further escalate the coalition's military campaign, underscore how the raging Yemen conflict is increasingly spilling across the border, threatening Saudi towns and villages.
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 GPC party to return to Arab fold. "The priority has been and still is to confront the forces of aggression".
The head of the Houthi's Ansarullah group, Abdel-Malek al-Houthi, has described Saleh's change of heart as "sedition", and appealed to him to show more wisdom and maturity.
The United Nations envoy to Yemen, Ismail Ould Cheikh Ahmed, and the ICRC urged the parties to avoid targeting civilians.
However, in a statement, Saleh's party, the GPC, ordered their supporters to defy Houthi's orders and to "defend their homeland, their revolution, and their unity".
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 conflict and a blockade by the coalition has also left more than 20 million people in need of humanitarian aid, created the world's largest food security emergency, and led to a cholera outbreak that is thought to have killed 2,211 people since April.