President-elect Donald J. Trump outlined an aggressive opening plan for his second term in an interview that aired on Sunday, vowing to fulfill his campaign promises to crack down on immigration and to pardon some of his most violent supporters on the first day of his new administration.

In his first sit-down broadcast network interview since being re-elected, Mr. Trump said he would move on the initial day of his term next month to pardon his backers who stormed the Capitol on Jan. 6, 2021, and to try to bar automatic citizenship for children born in the United States to immigrant parents.

Mr. Trump indicated that he would also fire the F.B.I. director, Christopher A. Wray, out of personal pique because “he invaded my home” and was not sufficiently sure at first whether his wound during an assassination attempt this year was caused by a bullet or shrapnel. Mr. Trump also left open the possibility that he would withdraw the United States from NATO and try again to overturn the Affordable Care Act.

But he also signaled that he would not take the most assertive position on several other issues. Speaking with Kristen Welker on “Meet the Press” on NBC, Mr. Trump said he would not seek to fire the chairman of the Federal Reserve or restrict the availability of abortion pills, and seemed to suggest he would not appoint a special counsel to investigate President Biden, as he once vowed. And though he vowed to end birthright citizenship, Mr. Trump said he would try to work with Democrats to spare immigrants brought to the country illegally as children, known as Dreamers, from deportation.

“I’m really looking to make our country successful,” Mr. Trump said when asked about investigating Mr. Biden and his family. “I’m not looking to go back into the past. I’m looking to make our country successful. Retribution will be through success.”

Mr. Trump sought to downplay fears of Kash Patel, the far-right loyalist he plans to nominate to take over the F.B.I., who has vowed to “come after” the president-elect’s perceived enemies and named about 60 people he considered “members of the executive branch deep state” as the appendix to a 2023 book.

“No, I don’t think so,” Mr. Trump said when asked if Mr. Patel would pursue investigations against political adversaries. But the incoming president left the door open to it. “If they were crooked, if they did something wrong, if they have broken the law, probably,” he said. “They went after me. You know, they went after me, and I did nothing wrong.”