TALLINN, Estonia — President Obama vowed on Wednesday to punish the Sunni militants whose videotaped beheadings of two American journalists he said had “repulsed” the world, saying the United States would lead a regional and international coalition to beat back the terrorists.

“Our objective is clear, and that is: degrade and destroy ISIL so that it’s no longer a threat, not just to Iraq but also to the region and to the United States,” Mr. Obama said, using an alternative acronym for the Islamic State in Iraq and Syria. He was speaking at a news conference here on the eve of a NATO summit meeting in Wales, as pressure built for him to articulate a broader military strategy to take on the ISIS militants.

“It’s not only that we’re going to be bringing to justice those who perpetrated this terrible crime against these two fine young men,” the president said. “The United States will continue to lead a regional and international effort against the kind of barbaric and ultimately empty vision” the group represents.

Mr. Obama’s strongly worded statement came after he drew criticism from allies and foes last week, when he said that he had not yet developed a strategy for confronting ISIS in Syria. American airstrikes in Iraq, the president said on Wednesday, had “borne fruit” by “blunting the momentum” of the militants in that country and averting the humanitarian disasters it had threatened to spark.