Saleh ruled Yemen for more than three decades until he was forced to resign following the Arab Spring uprising of 2011.
Those Houthi rebels' links to Iran led to a persistent air campaign from Yemen's neighbor Saudi Arabia, further plunging the country into violence and competing claims for the right to govern.
The Houthis accused Saleh of a coup on Saturday after he said he was open to talks with the Saudi-led military coalition backing Mr Hadi's government. He was killed during the.
The news that Saleh had been killed came just hours after Saudi Arabia made a decision to back Saleh, calling his fight against the Houthis a "popular uprising".
The Houthi claim come as tensions soar between the insurgents and the Saudi-led coalition, which imposed a crippling blockade on Yemen in response to a Houthi missile that was intercepted near Riyadh airport on 4 November.
As news broke of Saleh's death on Monday, the United Nations humanitarian coordinator for Yemen, Jamie McGoldrick, called for a pause in the fighting in Sanaa, noting that dozens of people had reportedly been killed and hundreds injured, including civilians.More news: Arsenal v Manchester United
But even without Saleh's loyalists, the rebels remain a powerful force and it is unclear how much the break with Saleh weakens them.
The rebel leader claimed many ordinary Yemenis were shocked by (Saleh's) calls for strife, combat, upsetting peace and security, and he says he tried in a fraternal and peaceful way to avoid the current conflict by talking (with Saleh).
However, in a speech late on Sunday, the day before his assasination, Saleh formally annulled his alliance with the Houthis and pledged to step up his fight. He remained in the country, however, and continued to wield political power from behind the scenes. This week's fighting reportedly left aid workers trapped inside a building and unable to administer support to civilians.
Meanwhile, Mr Hadi, Yemen's president, ordered his forces to retake the capital from the Houthis, an official from his office said.
The Houthis and forces allied to Saleh swept into the capital, Sanaa, in 2014.
"Saleh's actions in Yemen, in working with his former opponents the Houthis, were complicating numerous efforts at resolving the conflict", Harrison Akins, a researcher with the Howard Baker Center, told Newsweek.
He said they had targeted several media outlets affiliated with the former president, including the television channel for which he works, Yemen Today, which was owned by Saleh. In that critical moment I and my colleagues headed to evacuate our families from Hadah.