Vice President Abed Rabbo Mansour Hadi made the statement to officials of his party and diplomats in Sanaa, an official told The New York Times.
The United States is pressing the Saudis to make Saleh quit and keep him in Riyadh where he went for treatment after being injured in a rocket attack Friday, diplomats said.
U.S. officials insist Saleh must now be urged to agree to a deal under which he would give up power in exchange for immunity from prosecution and financial guarantees about his future, the diplomats told the British newspaper The Guardian.
The White House and State Department, and Saudi officials, had no immediate comment.
Washington stopped supporting Saleh in early April -- after long backing him, even in the face of widespread protests in Yemen -- because U.S. officials determined he was unlikely to bring about the required reforms and must therefore be eased out of office, U.S. and Yemeni officials said.
But U.S. officials were unable to influence Saleh, directly or indirectly, to step down.
President Barack Obama sent security adviser John Brennan to Saudi Arabia last week in the hope of finding a way of easing Saleh out, The New York Times said.
After Saleh went to Riyadh Saturday, Brennan spoke by phone with Hadi, who became acting president under the Yemeni Constitution, U.S. officials said.
U.S. Ambassador Gerald Feierstein met with Hadi Sunday, Yemen's state-run Saba News Agency reported.
But Saudi-owned al-Arabiya TV said the vice president was only a figurehead and Saleh's son, Ahmed, commander of the powerful Republican Guard, was actually running the country in his father's absence.
The younger Saleh is seen as corrupt, the Financial Times reported.