"The decision by (Saleh's) General People's Congress to take the lead and their choice to side with their people will free Yemen of. militias loyal to Iran", the statement carried by the official Saudi Press Agency said.
Yemeni President Abdrabbuh Mansur Hadi said all those who have identified a clear position in support of the popular uprising aimed at ending the coup and the restoration of the state "will all be partners in the present and future of Yemen".
Former Yemeni president Ali Abdullah Saleh has said he is ready for a "new page" in ties with the Saudi-led coalition fighting in Yemen if it stopped attacks on his country, in a move that could offer a pathway to end almost three years of war.
The Houthis retaliated to the Saleh advance by deploying four tanks on the streets of Sana'a in order to intimidate and terrorize the people and dissuade them from backing the former president.
Saleh went on to denounce the Houthi militia, which he accuses of being responsible for the humanitarian disaster inside the country, and he insisted that the Yemeni people are standing up for themselves to get rid of them.
The alliance between the Houthi rebels and former Yemeni President Ali Abdullah Saleh seems to be on the verge of a split.
"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.
Yemen fell into civil war in 2014, when Houthi rebels overran much of the country, including the capital Sanaa.
He added: "We will deal with them in a positive way and what happened to Yemen is enough".
On Saturday there were reports of further fighting in Sanaa, with explosions and gunfire concentrated in the southern suburb of Hadda where relatives of Mr Saleh live.
The army said government forces had repelled a Houthi attack on Mt. Sebahtal in the northern Saada province, with the support of coalition forces led by Saudi Arabia, according to 26sepnews.net, Yemen's national military website.
On Saturday, the Houthis fired three mortar rounds towards Tareq's house, while Saleh's supporters burned Houthi military vehicles; there are casualties from both sides. but there are no specific figures as the fighting is still ongoing.
For his part, leader of Huthi, Abdul Malik al-Huthi, has described Saleh's attitude as "sedition" and has been prepared for tribal arbitration, after warning that main beneficiary of this confrontation is Saudi coalition.
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.