The confirmation came after a Yemeni radio station announced earlier on Monday that Saleh had been killed during clashes in the Yemeni capital.
The Interior Ministry further said in its statement that Saleh had been creating "chaos" in the country through cooperating with "militias of aggression" and by providing help to "extremist militias."
The ministry added that the Yemeni forces, backed by fighters from the popular Ansarullah Houthi movement, were in full control of all positions previously held by Saleh's militias in Sana'a.
The statement also noted that conflicts, which had plagued Sana'a during past days, were actually over after death of Saleh.
"The Interior Ministry announces the end of the crisis of the treason militia and the killing of its leader and a number on his criminal partisans," it added.
Later in the day, Saudi-owned al-Arabiya television quoted sources in Saleh's party as confirming that he had been killed.
The news channel added that the sources had said Saleh was killed in fighting in Sana'a, but gave no further details.
Earlier on Monday, Saudi Arabia unleashed a fresh wave of aerial bombardments against targets in Yemen's capital in an apparent effort to support forces loyal Saleh.
Relations between the Houthi Ansarullah Movement and Saleh's forces deteriorated over the past weeks amid accusations from the rebels that Saleh was opening a back channel with the coalition through the United Arab Emirates, a coalition member, to turn against the Houthis.
Deif Allah al-Shami, a top Houthi politician, told The Associated Press that Saleh -- by his statements and actions on the ground -- had de facto joined the Saudi-led coalition. However, he said this spelled the end of Saleh, insisting the Houthis remain firmly in control.
"Saleh is over, this card is over," he said. "He is now part of the coalition and the aggression."
Saleh's family members, including his son Ahmed, who was once groomed to succeed his father and who led the powerful Republican Guards, have been in self-exile in the UAE since Saleh stepped down in the aftermath of the mass uprising against his rule during the 2011 Arab Spring.
Saleh and the Houthis are have always been unlikely allies. When Saleh was president he repeatedly went to war with the rebels in their northern heartland. In recent weeks, the Houthis have accused Saleh of trying to pull his forces from the front lines, while his supporters have complained about the Houthis monopolizing power.
Apparently confirming his break with the Houthis and aligning himself with Saudi Arabia, Saleh told Kuwait's al-Rai daily that "the era of the militias is over and there is no coexistence after today between a state and a quasi-state."
"Our natural orbit as Yemenis is the Gulf orbit," he added, referring to Saudi Arabia and the other Gulf Arab states. "Whatever differences we have with the Gulf countries, we will cooperate and agree."