WASHINGTON — The White House believes that Congress’s 2002 authorization of the Iraq war — and not just the 2001 authorization to fight Al Qaeda — provides a legal justification for President Obama’s air campaign against the Islamic State in Iraq and Syria, the Obama administration said Friday.

The White House has not issued a formal analysis of its legal thinking, but the disclosure adds to an evolving public understanding of its theory about the basis for the strikes against ISIS.

When the bombing began in August, Mr. Obama’s letters to Congress cited his constitutional powers as commander in chief. On Wednesday, Mr. Obama said he already had legal authority for the campaign, but would welcome specific congressional approval, too, and administration officials for the first time cited the 2001 authorization to use military force against those responsible for the 9/11 attacks for the campaign.

By claiming statutory authority, the administration sidestepped the War Powers Resolution, which requires deployments into hostilities to end after 60 days if Congress has not signed off. But public and background briefings for reporters this week mentioned only the 9/11 Authorization for the Use of Military Force, or A.U.M.F., and not the Iraq authorization, as did a statement the White House released after Mr. Obama’s speech.