The Saudi-led coalition welcomed Saleh's change of stance.
The fighting has killed dozens of people and wounded hundreds, according to the International Committee of the Red Cross, and raised concern of further casualties among civilians.
The wider Yemen conflict pits the Houthi-Saleh alliance against the Saudi-backed government of Abedrabbo Mansour Hadi.
Former Yemeni President Ali Abdullah Saleh said he was open to talks with the Saudi-led coalition fighting Iran-backed Huthi rebels, as his supporters fought the rebels in the capital, Sana'a.
But the head of the Houthis' Ansarullah group warned that the biggest victor from what he described as Saleh's "sedition" was the Saudi-led coalition.
Residents in Sanaa reported on Sunday that the Houthis appeared to be clawing back some territory lost to Saleh over the previous four days and Houthi tanks were deployed amid heavy gun battles in the city's central Political District.
For the Houthis to launch a missile from Yemen at the UAE, it would likely have to fly over Saudi Arabia's vast southeastern desert in order to reach Abu Dhabi. Otherwise, he says that the government must impose security in tandem with the people, if the militias (supporting Saleh) don't put down their arms. 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.
Saudi forces have been widely accused of committing war crimes during the campaign in the country, where reports on the ground suggest they have blown up global hospitals, funerals, schools, and weddings.
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 to the brink of starvation.
The United Arab Emirates' state-run news agency is denying a claim that a Yemeni missile targeted its under-construction nuclear plant.
"The missile force announces the launching of a winged cruise missile. towards al-Barakah nuclear reactor in Abu Dhabi", noted a statement on both websites. It was the deepest strike inside the kingdom since the war between the Saudi-led coalition and the Houthis and their allies began in March 2015.