WASHINGTON — The Obama administration said Wednesday that it needed no new approval from Congress to launch an open-ended air war in both Syria and Iraq against the group known as ISIS because the campaign is covered by the existing authorization to use military force against the perpetrators of the Sept. 11, 2001, terrorist attacks — that is, Al Qaeda.

Until now, the administration had cited only the president’s constitutional powers as commander in chief as the basis for recent airstrikes against the Islamic State in Iraq and Syria. But its new rationale raised questions about the factual basis behind its assertion that the 2001 authorization to use military force, known as the A.U.M.F., covers ISIS.

While ISIS grew out of a branch of Al Qaeda that sprang up in Iraq after the American invasion there in 2003, the two groups fell out over the past year over strategy and control. Last February, the leader of the original Al Qaeda, Ayman al-Zawahri, excommunicated ISIS, declaring that it “is not a branch of the Al Qaeda group.”

“As I understand it, the A.U.M.F. covers Al Qaeda and its affiliates,” said Will McCants, a Middle East specialist at the Brookings Institution. “The Islamic State was an Al Qaeda affiliate, and it is not anymore. So technically, the A.U.M.F., as I understand it, would not cover the Islamic State.”