"We vow to our brothers and neighbors 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".
The Saudis want to restore the internationally-recognised government of President Abd Rabbu Mansour Hadi, who was forced into retreat and then exile by the fighting.
"I call on our brothers in neighbouring countries ... to stop their aggression and lift the blockade ... and we will turn the page", Mr Saleh said in a televised speech on Saturday, according to Agence France-Presse.
"We will deal with them in a positive way and what happened to Yemen is enough", he added. There has been no official word on casualties but the International Committee of the Red Cross (ICRC) said that dozens were killed and hundreds were wounded in the fighting.
The coalition, which has fought Saleh and the Iran-backed Houthis since 2015, last month imposed a total blockade on the impoverished country after a rebel missile was shot down near Riyadh.
"The uprising in Yemen's capital Sanaa is the sign of an awakening of the nightmare", UAE's Minister of State for Foreign Affairs Anwar Gargash said on Twitter. He fought six wars against the Huthis when he was president, but joined forces with them to take over the capital in 2014.
The coalition accuses Saleh, who heads the General People's Congress party, of betraying his Arab neighbors by joining forces with the Houthi rebels. "The priority has been and still is to confront the forces of aggression".
The Houthis' Ansarullah group, in a statement issued on its Twitter account, described the clashes as "regrettable".
Earlier, Saleh's General People's Congress (GPC) party, accused the Houthis of failing to honor the truce and said in a statement on its website that the Houthis bear responsibility for dragging the country into a civil war.
It also called on supporters, including tribal fighters, to "defend themselves, their country, their revolution and their republic".
"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.
In March 2015, warplanes from Saudi Arabia, the UAE, Kuwait, Bahrain, Qatar and other allies began airstrikes on rebel positions in Yemen.