The call came as his supporters battled Houthi fighters for a fourth day in the capital Sanaa as the two sides traded blame for a rift between allies that could affect the course of the civil war, Reuters reported.
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. Arab media is reporting that the former president's supporters have gained control of key government installations in the capital, including the defense ministry, the interior ministry and Sana'a Airport.
Mr Saleh, who led Yemen for more than 30 years, was deposed in a 2011 uprising.
The Houthi rebels denounced what they described as "sedition", meaning Saleh's behaviour towards the Saudi coalition.
The Saudi-led coalition, consisting of several Arab-Sunni states, intervened in neighbouring Yemen to push back Houthi rebels and has since been trying to reinstate the government of President Abd-Rabbu Mansour Hadi.
Former president Saleh and the Yemeni military fought the Houthi rebels five times from 2005 to 2014, before becoming allies after the Saudi-led coalition took military action in March 2015 to restore President Hadi to power, who had been ousted and imprisoned by the Houthis.
"It is not odd or surprising that Saleh turns back on a partnership he never believed in", the group's political bureau said in a statement.
There was no immediate word on casualties.
Fighting between rebel groups has erupted in Sanaa in recent days, leading to dozens of deaths, officials from both sides told CNN.
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.
"The GPC appealed to the army and security forces to remain neutral in the conflict".
"Air defence intercepted a ballistic missile, fired by the Houthis towards Khamis Mushait", Arabiya said on its Twitter account, without giving details.
In response to Saleh's speech, Houthi leader Abdel-Malek al-Houthi stressed the need for dialogue in another televised appearance in Saturday, and called on Saleh to "be more mature".
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.