After the clashes in August, both sides tried to calm the situation because they usually fight on the same side against the pro-government forces and the Saudi-led coalition, so things between them were quiet until Wednesday.
On Thursday, Houthi threatened to retaliate again over a blockade imposed by the coalition, after a November 4 rebel missile attack that was intercepted near Riyadh global airport.
Thursday night's violence in Sanaa came 24 hours after clashes at the Saleh Mosque in the capital killed nine Houthi rebels and five Saleh supporters.
In a televised speech on December 2, Saleh called on the Saudi-led coalition to pave the way for an end to nearly three years of war by stopping attacks and lifting a siege on the country.
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.
In 2011, Yemen fell into chaos after an uprising deposed Saleh.
However, the Houthis were less open to Mr Saleh's idea.
Diab says the Saudi-coalition forces are not too far from the capital, and the Houthis have become widely despised due to shortages of food, water, medicine and money.
A source in Saleh's forces said Houthi fighters were positioned around the residences of two of the ex-president's nephews.
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.
"It is not unusual or surprising that Saleh turns his back on a partnership he never believed in", the group's political bureau said in a statement.
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". Tensions between the heretofore allies have grown in recent months with Saleh supporters accusing the Houthis of trying to monopolize power.
He told Yemenis all across the country that if they support him, "to defend the nation, the republic and the revolution".
A statement from Saleh's GPC appealed on Saturday to security and military forces and all public employees to be neutral and not to implement instructions given by the Houthis in all provinces.
The war in Yemen is one of the worst humanitarian crises in the world, killing at least 10,000 people and leading to widespread hunger and disease.
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