Houthi-controlled al-Masirah TV cited the interior ministry as announcing the "end of the crisis of the treason militia and the killing of its leader".
Footage on social media appeared to show the former leader's body wrapped in a blanket with a large wound on the side of his head.
Saleh was once allied with the rebel Houthis, a Shiite group linked with Iran.
On this regard, Qatari Minister of Foreign Affairs Mohammed bin Abdul Rahman Al-Thani said on Thursday, on the sidelines of the third edition of the Mediterranean Dialogues Forum, that Abdullah Saleh's insult to Qatar is unjustified.
Saleh's supporters managed on Saturday to seize control of several embassies and government buildings from the Houthis.
Residents in Sanaa told Reuters that Houthi fighters blew up Saleh's house in the center of the city.
A senior official with Yemen's internationally-recognized government confirmed to The Associated Press that Saleh had been killed, sending video purportedly showing Saleh's body being carried away by a group of armed men chanting, "Allahu akbar".
The former Yemeni president's break with the Houthis came after five days of bitter clashes around the capital, Sana'a, between his supporters and those of the Iranian-backed Houthi militia.
It was a grisly end for a figure who was able to rule the impoverished and unstable country for more than three decades and remained a powerhouse even after he was ousted in a 2011 Arab Spring uprising.
Saleh loyalists and rebel fighters continued to clash on Saturday afternoon in Sanaa, where violence has left at least 40 fighters dead or wounded since Wednesday according to rebel chief Abdulmalik al-Huthi.
In this January 3, 2017 file photo, tribesmen loyal to Houthi rebels chant slogans during a gathering aimed at mobilizing more fighters into battlefronts to fight pro-government forces.
Yemen's war has killed more than 10,000 people since 2015, displaced more than two million people, and caused a cholera outbreak infecting almost one million people. Iran supports the Houthis but denies arming them.
Senators anxious about fake comments in FCC plan to change net neutrality
As Republicans now hold a majority of the FCC's five seats, the order to repeal the net neutrality rules is expected to pass. Twenty-eight USA senators have asked that the vote be postponed due to the allegations of fraud dismissed by Chairman Pai.