“The president of the United States is allowed to have whatever conflicts he or she wants, but I don’t want to do that,” Mr. Trump said. But he said that Mr. Kushner, who is an observant Jew, “could be very helpful” in reconciling the longstanding dispute between the Israelis and the Palestinians.

“I would love to be able to be the one that made peace with Israel and the Palestinians,” Mr. Trump said, adding that Mr. Kushner “would be very good at it” and that “he knows the region.”

“A lot of people tell me, really great people tell me, that it’s impossible — you can’t do it,” Mr. Trump added. “I disagree. I think you can make peace.”

“I have reason to believe I can do it,” he added.

Mr. Trump spoke only in general terms about foreign policy. He said the United States should not “be a nation builder,” repeated his line from the campaign that fighting the war in Iraq was “one of the great mistakes in the history of our country,” and said he has some “very definitive” and “strong ideas” about how to deal with the violent civil war raging in Syria. He declined to say what those ideas are despite several requests to do so.

“We have to end that craziness that’s going on in Syria,” he said.

The president-elect said that he had talked with President Vladimir V. Putin of Russia since winning the election, but he did not elaborate. He said it would be “nice” if he and Mr. Putin could get along, but he rejected the idea that any warming of relations would be called a “reset,” noting the criticism that Mrs. Clinton received after her attempts at bettering relations between the countries failed.

“I wouldn’t use that term after what happened,” Mr. Trump said.

Mr. Trump made a forceful defense of Mr. Bannon, whom he named as his chief strategist and who has drawn charges of racism and anti-Semitism. This summer, Mr. Bannon called Breitbart News, the website he led, “the platform for the alt-right,” a white nationalist movement.