"The Interior Ministry announces the end of the crisis of militias and the killing of their leader and a number of his criminal supporters", an anchor from Houthi-affiliated Al-Masirah television said, referring to armed supporters of Saleh.
Unverified footage circulated by Yemeni social media users on Monday appeared to a show corpse resembling Saleh.
An urgent meeting will be held soon in Iran between Qatar's Minister of State for Defense Khalid al-Attiyah, Commander of the Iranian Revolutionary Guard Corps (IRGC) Mohammad Ali Jafari, and representatives of Hezbollah and Houthi rebels, according to informed sources.
Witnesses say that fighting has subsided in the Yemeni capital Sanaa hours after the announcement of the death of Yemen's former president Ali Abdullah Saleh.
The source said that clashes had renewed on Saturday between the Houthis and Saleh's supporters in the Yemeni capital Sana'a.
In other areas like Fag Attan, Saleh's forces are still surrounded by Houthis.
The Saudi-led coalition had been fighting both the Shiite Houthi rebels and Saleh's party in Yemen since March 2015 to support the internationally-recognized government led by President Abd-Rabbu Mansour Hadi.More news: Tunisia coach Maaloul targets World Cup opener against England
"I can hear heavy shelling outside now and know it is too imprecise and too pervasive to guarantee that any of us are safe", she said.
Saleh said Saturday that he was ready to talk to the Saudi-led coalition if it lifts a crippling blockade imposed on the impoverished country last month after a rebel missile was shot down near Riyadh.
United Nations humanitarian affairs chief Mark Lowcock said on Friday that the Saudi-led military coalition must fully lift its blockade on Yemen, where 7 or 8 million are "right on the brink of starvation", Reuters reported.
Mr Saleh ruled Yemen for more than 30 years. He remained in the country, however, and continued to wield political power from behind the scenes.
Internal rifts have shaken the fragile alliance between the Houthis and Saleh loyalists, who joined ranks in 2014 to seize Sanaa.
Saudi Arabia views the Houthis as an Iranian proxy located just next door. His party's alliance with the Houthis disintegrated and the two sides fought bloody clashes in Sanaa, the capital, that killed dozens of people.