President Trump offered up a brief preview of his priorities for meetings with international leaders in the coming weeks, suggesting Sunday that the North American Free Trade Agreement (NAFTA) could be on the chopping block in the near future.

“We’re going to start some negotiations having to do with NAFTA,” Mr. Trump said in his opening remarks at a White House event to swear in senior administration officials. “I ran a campaign somewhat based on NAFTA. But we’re going to start renegotiating on NAFTA, on immigration, on security at the border.”

Mexico, the president went on, has so far been “terrific” in their conversations, and Mexican President Enrique Peña Nieto -- who spoke with Mr. Trump by phone Saturday -- has been “really very amazing.”

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Mr. Trump ran a campaign in 2016 promising to rip up international trade deals, calling them a “disaster” and blasting them as reasons for the lowering employment opportunities in the manufacturing industry.

In an interview on CBS’ “60 Minutes” in 2015, the then-candidate promised to revamp NAFTA or “we will break it.”

“Every agreement has an end,” he said at the time. “Every agreement has to be fair. Every agreement has a defraud clause. We’re being defrauded by all these countries.”

Mr. Trump’s pick for commerce secretary also listed a second look at NAFTA as a top priority.

In his confirmation hearing last week, billionaire investor Wilbur Ross said the trade agreement was “logically the first thing for us to deal with.”

“We must solidify relationships in the best way we can in our own territory before we go off to other jurisdictions,” he said. “That will be a very, very early topic in this administration...I think all aspects of NAFTA will be put on the table.”

The discussions to overhaul the 23-year-old trade deal could start as early as next week: the president is scheduled to meet with the Mexican president on Jan. 31, according to White House press secretary Sean Spicer.

And Mr. Trump said Sunday at East Room ceremony that he has also scheduled a meeting with Justin Trudeau, the prime minister of Canada, the third country directly impacted by NAFTA.

Mr. Trump is also expected to meet with British Prime Minister Theresa May on Friday, following an appearance May will make at a retreat in Philadelphia for Congressional Republicans.

The president, in his wide-ranging remarks to his senior White House staff, briefly hinted at running for re-election in 2020.

“We are going to do some great things over the next eight years,” he said, before stepping aside to allow Vice President Mike Pence to swear in his administration officials.

Mr. Trump also weighed in on the traditional letter every departing president gives to his successor, which he held up during the ceremony to show the audience.

“We will cherish that,” he said, before ribbing that “we won’t even tell the press what is in that letter.”