“As I’ve said before, if we can get an A.U.M.F. done that ensures our commanders have the flexibility they need to defeat ISIS, I want to move it,” Mr. Royce said in a prepared statement. “But ultimately, it is going to be up to President Obama to lead. Containment has failed. The administration already has the authority it needs to take the fight to these radical Islamist terrorists, and it needs to step up.”

The White House press secretary, Josh Earnest, said he welcomed the move but questioned whether Mr. Ryan could actually get the measure through the House. “He has not made hardly any progress that anybody can detect in passing an authorization to use military force against ISIL,” Mr. Earnest said.

Congress voted to authorize force in 2001, to respond to the Sept. 11 terrorist attacks, and in 2002, for the invasion of Iraq. While the Obama administration has long said those measures provide all the authority it needs for new uses of force, Mr. Obama has also asked Congress as recently as last month for another bill to confront the Islamic State.

Republicans — who, like Democrats, still feel burned by their vote in 2002 to authorize the war in Iraq — have been reluctant to debate the matter and to give Mr. Obama more war powers.

Mr. McConnell has repeatedly rejected the idea of a new authorization, saying he does not wish to restrain the next president with such a measure.