“Our focus in Syria is not to solve the entire Syria situation, but rather to isolate the areas in which ISIL can operate,” he added, using an alternative name for the Islamic State.

That statement appeared somewhat at odds with a recent memo sent to the White House by Defense Secretary Chuck Hagel, in which he criticized the administration’s Syria policy for failing to connect the campaign against the Islamic State to the broader struggle against President Bashar al-Assad.

Mr. Hagel wrote that unless the United States clarified its intentions against the Assad regime, it would fail to enlist allies like Turkey and France for the battle against the Islamic State in Syria, since those countries are intent on ousting Mr. Assad. Other officials said that in internal debates, Mr. Hagel has not advocated taking a strong line against Mr. Assad, and in fact has echoed the Pentagon’s resistance to going to war with the Syrian government.

That will be one of the issues likely to come up in a congressional debate over authorization. Before the election, Congress passed limited authorization to pay for the training and equipping of Syrian rebels. Now the White House is seeking an authorization to use military force that would be tailored to a prolonged fight against ISIS.

Until now, the White House had justified its airstrikes in Iraq and Syria under two existing laws: a 2001 authorization passed after the 9/11 attacks, which Mr. Obama has invoked to carry out drone and missile strikes against suspected terrorists in Yemen and Somalia, and a 2002 authorization sought by President George W. Bush for the Iraq war.

“The idea is to right-size and update whatever authorization Congress provides to suit the current fight rather than previous fights,” Mr. Obama said. “We now have a different type of enemy.”

Lawmakers welcomed the announcement, even as they noted it would set off complicated political crosscurrents in both parties. Many lawmakers were privately relieved that the White House did not petition Congress before the midterm elections.