Scoffing at pressure to quit at a time of growing insecurity, as highlighted by the blast at an ammunitions plant in Jaar, Saleh challenged his opponents to leave the country instead, in remarks published on Tuesday.
His remarks came after Washington warned on Sunday that the fall of Saleh would pose a "real problem" for the United States.
"I think it is a real concern because the most active and at this point perhaps the most aggressive branch of al Qaeda, al Qaeda in the Arabian Peninsula, operates out of Yemen," said US defence secretary Robert Gates.
With the district falling into the hands of al Qaeda on Sunday, around 30 armed and hooded gunmen looted the factory and made off in four vehicles with cases of weapons, witnesses said.
Officials have said explosions and a huge fire engulfed the factory as the villagers were inside helping themselves to remaining ammunition and guns left behind after the raid on the plant by the al Qaeda fighters.