The Saudi-led coalition welcomed Mr Saleh's change of stance.
"I call on our brothers in neighbouring countries.to stop their aggression and lift the blockade. and we will turn the page", Saleh said.
The fighting subsided by the afternoon as Saleh supporters secured control.
Stressing that Yemen's interests lie in avoiding sedition, the Houthi leader called on citizens and tribal fighters to focus on the battle against the invading Saudi regime and stay away from any provocative acts.
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. Aid groups say dozens of people have been killed in fighting between the two sides in recent days.
The clashes, which erupted late Wednesday near the Saleh Mosque in the capital, killed nine Houthi rebels and five supporters of former president Saleh, according to multiple medical sources. The former president's alliance with the Shiite rebels, who are presumed in Riyadh to be a proxy force of Iran, was perceived in the Arab kingdom as a betrayal of Sunni Islam.
For his part, Houthi leader Abdel Malek al-Houthi called on Saleh to end what he called "the sectarian strife" that he has instigated, and threatened to take action against his supporters militarily if he does not.
Security forces loyal to Saleh joined forces with the Houthis in 2014, and they went on to capture swathes of territory together and fight government forces backed by the Saudi-led coalition.
Saleh may be a noticeable player in the Yemeni conflict, but one should not overestimate the role he plays, Sergey Balmasov, senior analyst at the Centre for Crisis Society Studies, told RT. "The escalation of violence is overarching there". Moreover, Yemen, which was already poorest country in Middle East, is on brink of starvation, with three-quarters of its 28 million people dependent on humanitarian aid.
He added that some speculators claim that Saleh's statements are actually a proposition by Saudi Arabia to roll down the hostilities in a manner which would save face. "The reserves they accumulated during the fat years are melting like a snowball in the sun", he explained.
The civil war has left 10,000 dead, displaced to two million people and caused an epidemic of cholera that has affected almost anor million.
Saleh agreed to leave presidency in 2012, n 33 years in front of Yemen, after months of popular protests and worldwide pressure (including that of its neighbours) to prevent anor civil war being unleashed as in Libya or Syria.