President Obama showed a flash of anger Monday with Republican critics of his anti-terrorism strategy, saying he is “too busy” to engage in a rhetorical debate with them.

“What I’m not interested in doing is posing or pursuing some notion of American leadership, or American winning or whatever other slogans they come up with, that has no relationship to what actually is going to work to protect the American people” and America’s allies, Mr. Obama said at a news conference in Turkey. “I’m too busy for that.”

The president was addressing a question about critics of his strategy for defeating the Islamic State, in the wake of the terrorist attacks in Paris last week.

“I can’t afford to play some of the political games that others may,” Mr. Obama said. “We’ll do what’s required to keep the American people safe. It’s entirely appropriate for us in a democracy to have a debate about these issues. If they think that somehow their advisers are better than the chairman of my Joint Chiefs of Staff, and the folks who are actually on the ground, I want to meet them.”