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.
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 coalition had also imposed a blockade on the country, allowing occasional humanitarian access, with the aim of reinstating the internationally recognised government of Mr Saleh's successor, Abed Rabbo Mansour Hadi.
"We vow to our brothers and neighbours that, after a ceasefire is in place and the blockade is lifted. we will hold dialogue directly through the legitimate authority represented by our parliament", he said.
"We will deal with them in a positive way and what happened to Yemen is enough", he added.
There was no immediate word on casualties.
The UN urged the coalition in a statement Saturday to "fully lift" the blockade on Yemen's red sea ports saying that partial lifting only "slows the collapse toward a massive humanitarian tragedy costing millions of lives".
Later in the day, Saleh said he was ready for a "new page" in relations with the Saudi-led coalition pounding Yemen if it stopped attacks on his country.
The Saudi-led coalition welcomed Saleh's change of stance. 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 Saudi-led coalition has fought Saleh loyalists and the Iran-backed Houthis rebels on behalf of the government of president Abdrabu Mansur Hadi since March 2015.
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".
"I appeal to the leader Saleh to show more wisdom and maturity. not to heed incitement calls, and help restore security to the country through cooperation", al-Houthi further said.
"It demands the anti-government forces in Yemen to desist from attacks against the Kingdom of Saudi Arabia", the FO added.