"I call on our brothers in neighboring countries.to stop their aggression and lift the blockade. and we will turn the page", the former president said in a televised speech.
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 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.
The fighting subsided by the afternoon as Saleh supporters secured control.
Yemen's former president Ali Abdullah Saleh has declared this Saturday ready to negotiate with Saudi Arabia-led coalition against which his forces have been fighting for two and a half years.
However, the leader of the Houthis, Abdul Malik al-Houthi denied in a TV address on Saturday that his fighters had stormed the mosque, attributing the reason behind the clashes to some militias that want to create chaos in Sana'a.
In 2015 he fled to Saudi Arabia, which used its military force in a bid to place him back in power in Yemen. They spoke on condition of anonymity, fearing reprisals.
A statement from Saleh's General People's Congress Party said three guards were killed when Houthi forces attacked the house of Tarek Saleh, Ali Abdullah Saleh's nephew, adding that they also besieged the residence of Ibrahim Sharaf, a party member and foreign minister of the Sanaa-based government.More news: Syria fires missiles at Israeli aircraft after Israeli missiles hit near Damascus
Saudi Arabia says that it has intercepted a second missile fired towards the country by Houthi rebels in Yemen.
The clash between Saleh's supporters and the Houthis underscores the complex situation in Yemen, one of the poorest countries in the Middle East, where war between Houthis and the Saudi-backed Hadi has caused one of the worst humanitarian catastrophes in recent times. The country has since fallen into chaos and Mr Saleh later joined the Houthis to drive Mr Hadi out of the capital in 2014.
A statement from Saleh's party called for its loyal armed tribes and supporters to fight against Houthis.
The United Nations has warned that the country faces mass starvation unless the Saudi-led coalition allows more food aid to enter the impoverished country.
Abdel-Malek al-Houthi, the leader of the rebels, called on Saleh to "show more wisdom and maturity" in a separate statement.
Hussein Badreddin al-Houthi, founder of the Houthi movement, was killed by Saleh government forces in 2004.
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.