Saleh's calls came during a live television address on Saturday, in which he vowed to change if Saudi Arabia stopped its "aggression" and lifted restrictions on Yemen, calling for "opening a new page with neighboring countries".
The coalition accuses Iran of trying to expand its influence into Arab countries, including Yemen by aligning themselves with the Houthis and Mr Saleh.
He says that the Yemeni people in Sana'a and in all the provinces have carried out an uprising against the aggression (of the Houthis) toward the nation in the three years after (President Abdrabbu Mansour Hadi) Hadi fled the country, during which time salaries have not been paid, food, water and medicine have become scarce, insecurity has reigned, and children have been drafted to fight.
The Saudi-led coalition fighting in Yemen said on Saturday it was confident that leaders of former Yemeni President Ali Abdullah Saleh's General People's Congress Party (GPC) would return to the Arab fold.
"It demands the anti-government forces in Yemen to desist from attacks against the Kingdom of Saudi Arabia", the FO added.
Violence in Sanaa has left at least 40 fighters dead or wounded since Wednesday, rebel chief Abdul Malik al-Houthi said, as Saleh loyalists and rebel fighters continued to clash on Saturday afternoon.
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.
Street fighting in the war-wracked country comes amid heightened regional tensions, most notably after Houthi rebels early last month launched a missile that was intercepted near the Saudi capital.
A coalition statement said the decision to "take the lead and to side with their people will free Yemen of. militias loyal to Iran".
A statement from Saleh's party called for its loyal armed tribes and supporters to fight against Houthis.
"It is happening in coordination with it", referring to the Saudi-led coalition".
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.
Hussein Badreddin al-Houthi, founder of the Houthi movement, was killed by Saleh government forces in 2004. 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.