Having occupied crucial sections of Syria over the past year and more recently seizing vast areas of Iraq, the Islamic State in Iraq and Syria controls territory greater than many countries and now rivals Al Qaeda as the world’s most powerful jihadist group.

even as he expressed strong opposition to deploying American ground troops.

The president is still wrestling with a series of challenges, including how to intervene without aiding President Bashar al-Assad, and how to enlist potentially reluctant partners like Turkey and Saudi Arabia.

“The president has now declared that defeating ISIL is his objective,” he said. “That’s a good start. But Americans don’t want a lecture. They want a plan — a credible, comprehensive plan to deal with this menace that clearly wants to harm us here at home, and that is only becoming stronger by the day.”

Mr. Obama’s speech to the nation, on the eve of the 13th anniversary of the Sept. 11, 2001, terrorist attacks,

The harrowing images, captured on video and circulated around the world, have turned American public opinion in favor of military action against the militants, recent polls show, and appear to have moved a president who had long resisted military engagement in Syria. And the United States has conducted airstrikes against ISIS in Iraq.