President Trump did not rule out seeking a third term in office on Sunday, telling NBC News that he was “not joking” about the possibility and suggesting there were “methods” to circumvent the two-term limit laid out in the Constitution.

In wide-ranging remarks to “Meet the Press,” Mr. Trump said “a lot of people” wanted him to serve a third term, described himself as “pissed off” at President Vladimir V. Putin of Russia and vowed to impose tariffs on global rivals, according to a transcript of the interview provided by the network.

“A lot of people want me to do it,” he said to the program’s host, Kristen Welker, about the possibility of a third term. “But we have — my thinking is, we have a long way to go. I’m focused on the current.”

Any attempt to seek a third term would run afoul of the 22nd Amendment, which begins, “No person shall be elected to the office of the president more than twice.”

On Sunday, after the release of the interview, the White House reiterated Mr. Trump’s point that he was focused on his current term, and added that it was “far too early to think about” the idea.

“Americans overwhelmingly approve and support President Trump and his America First policies,” Steven Cheung, the White House communications director, said in a statement. He added that Mr. Trump was focused on “undoing all the hurt” done by the Biden administration and “Making America Great Again.”

Mr. Trump has often mused about the idea of a third term, particularly in rallies and speeches that have delighted his supporters, though he has often treated it more as a humorous aside. The interview was the first time that Mr. Trump indicated that he was seriously considering the idea, which his allies have continued to amplify. Already he has likened himself to a king, shown an affinity for autocratic leaders and displayed governance tactics constitutional experts and historians have compared to authoritarianism.

Three days after Mr. Trump was sworn in for the second time, Representative Andy Ogles of Tennessee proposed an amendment to the Constitution that would make Mr. Trump eligible for a third term. Such a measure would be extraordinarily difficult: Constitutional amendments require approval by a two-thirds vote of Congress and then the ratification of three-fourths of the states.

In the interview, Ms. Welker noted that she had heard him joke about serving a third term a number of times. Mr. Trump made it clear he considered it a real possibility.

“No, no I’m not joking,” he said. “I’m not joking.”

Ms. Welker asked Mr. Trump whether he had been presented with plans, and he said that he had not — but added that there were “methods which you could do it.”

Ms. Welker suggested one possibility: having Vice President JD Vance at the top of the ticket in 2028, only to pass the office on to Mr. Trump after winning. Mr. Trump acknowledged “that’s one” way it could happen.

“But there are others too,” he said. “There are others.”

Mr. Trump declined to say what those could be.

Derek T. Muller, a law professor at the University of Notre Dame and a scholar in election law, said there has been a dissenting view about the provision of the 22nd Amendment — which focuses on being “elected” president without addressing the idea of ascending to the office. However, he said, such a route would be complicated by the 12th Amendment.

Mr. Muller pointed out that the 12th Amendment states that “no person constitutionally ineligible to the office of president shall be eligible to that of vice-president of the United States.”

Mr. Muller said he very much doubted that would provide a path to a third term for Mr. Trump.

“You’d have to have so many pieces fall into place for this even to be practically viable, on top of this complicated legal theory,” he said.

In his remarks to Ms. Welker, the president also leveled his strongest criticism to date against Mr. Putin, threatening to impose “secondary tariffs” on Russia’s oil if the country thwarted negotiations on a cease-fire deal with Ukraine that would stop the fighting.

The comments signaled growing impatience with the negotiations. Mr. Trump said that tariffs of 25 to 50 percent on Russian oil could be imposed at “any moment” and that he planned to speak with his Russian counterpart this week.

“If Russia and I are unable to make a deal on stopping the bloodshed in Ukraine, and if I think it was Russia’s fault — which it might not be — but if I think it was Russia’s fault, I am going to put secondary tariffs on oil, on all oil coming out of Russia,” Mr. Trump said.

Mr. Trump has previously referred to secondary tariffs as levies on imports from countries that purchase products from a nation he’s targeted in his foreign policy. The White House did not immediately respond to a request for comment.

The comments were notable given the steps that Mr. Trump has taken to align himself with Mr. Putin, despite the United States’ support for Ukraine since Russia’s full-scale invasion more than three years ago. Since taking office, Mr. Trump has declined to acknowledge that it was Russia who started the war, falsely declared President Volodymyr Zelensky of Ukraine a “dictator,” but not Mr. Putin, and accused Mr. Zelensky of not wanting peace.

Mr. Trump’s remarks also underscored his increasing promise to use tariffs to compel countries to bend to his domestic and foreign policy goals. In the same phone call, he said he would consider secondary tariffs on Iran if it did not reach a deal with the United States to ensure it did not develop a nuclear weapon, Ms. Welker said.

Mr. Trump told Ms. Welker that he was “very angry, pissed off” at Mr. Putin for questioning the credibility of Mr. Zelensky, and for discussing the prospect of new leadership in that country. Mr. Trump suggested that such comments could set negotiations back, and that they were ”not going in the right location.”

“New leadership means you’re not going to have a deal for a long time, right?” Mr. Trump said.

Russia and Ukraine have agreed to a limited truce, but that has fallen short of the complete pause in combat that Trump administration officials have sought, with Ukraine’s support. The limited cease-fire remains tenuous as Russia seeks more concessions and Ukraine has expressed doubt that a truce would be upheld.

On negotiations about Iran’s nuclear capabilities, Mr. Trump said officials from both countries were “talking,” according to NBC’s account of Ms. Welker’s call with the president, although he raised the prospect of military action if economic and other measures do not succeed.

“If they don’t make a deal,” Mr. Trump said about Iran, “there will be bombing. It will be bombing the likes of which they have never seen before.”

Earlier this month, Mr. Trump sent a letter to Iran’s supreme leader, Ayatollah Ali Khamenei, urging direct negotiations with the government in Tehran on a deal to curb the country’s advancing nuclear program. The letter said Mr. Trump preferred diplomacy over military action.

Mr. Trump’s raising of secondary tariffs on oil from Russia and Iran was the latest example of the president’s interest in using the prospect of economic pressure on third-party nations.

Last week, he issued an executive order on Monday to crack down on countries that buy Venezuelan oil by imposing tariffs on the goods those nations send into the United States, claiming that Venezuela has “purposefully and deceitfully” sent criminals and murderers into America.

Mr. Trump called the new levies he threatened on buyers of Venezuelan oil “secondary tariffs,” a label that echoed “secondary sanctions” — penalties imposed on other countries or parties that trade with nations under sanctions.

Some trade and sanctions experts said existing secondary sanctions associated with countries such as Russia and Iran already were not well enforced, and questioned whether the United States would have the capacity to pull off new tariff-based penalties.