The infighting threatens to unravel the fragile alliance that controls the capital and has been battling the Saudi-backed government of President Abed Rabbo Mansour Hadi in Yemen's war.
"It's been like a street war", they said, adding that ambulances have been ferrying the wounded to hospitals.
Khattar Abou Diab, who teaches political science at the University of Paris, tells VOA that former president Saleh has a "strong political instinct" and that he made his move against the Houthis at a time when the situation on the ground is favorable. He said his offer would require Riyadh to stop attacks on Yemen.
Officials working at the TV station say Houthis raided its headquarters.
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.
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Wali and another student rushed to his aid, hiding from the gunmen for nearly an hour before they were rescued by security forces. Noor Wali, a 19-year-old student at the institute, described a terrifying ordeal that began when he was woken by gunshots.
Saleh called for a joint ceasefire to be agreed on by his loyalists and the Houthi militia, after clashes entered their fourth day and hae resulted in the deaths of at least 80 people.
Mr Hadi, in a statement after a meeting with his advisors, also said he was ready to work with Mr Saleh against the Houthis.
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 Houthi allied themselves with the forces loyal to Saleh and have fought a devastating war against forces loyal to Hadi and his foreign backers.
He said that the Houthi militias had been seeking "in various ways to reproduce the model of the mandate of the Iranian jurist, and bet on the decision of Yemen and its sovereignty to the malignant evil and mischief in Qom and Tehran".
"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.
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The first five holes I hit a lot of good shots and felt like I had a good rhythm and a couple birdies early on. While he had his chances, he didn't make another birdie and finished with a bogey after a poor drive.
But Saleh's message didn't sit well with the Houthis, whose spokesman called his remarks "a coup against our alliance and partnership".
However, in a statement, Saleh's party, the GPC, ordered their supporters to defy Houthi's orders and to "defend their homeland, their revolution, and their unity".
The Houthi group leader, Abdel-Malek al-Houthi, had earlier appealed to Mr Saleh to avoid any escalation, saying that the crisis would only serve Yemen's enemies.
The conflict and a blockade by the coalition has also left more than 20 million people in need of humanitarian aid, created the world's largest food security emergency, and led to a cholera outbreak that is thought to have killed 2,211 people since April.
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And I love how Japan apparently sees Batman: as an unstoppable flood of psychedelic, weird villains and mythic characters. Batman Ninja is yet to be given a release date, but it is expected to arrive in 2019.