"As we discussed during your visit in April, there is growing frustration in the United States that some allies have not stepped up as promised," Mr. Trump wrote to Chancellor Angela Merkel of Germany in a particularly pointed letter, according to someone who saw it and shared excerpts with The New York Times. "The United States continues to devote more resources to the defense of Europe when the Continent's economy, including Germany's, are doing well and security challenges abound. This is no longer sustainable for us."

"Growing frustration," Mr. Trump wrote, "is not confined to our executive branch. The United States Congress is concerned, as well."

The president's complaint is that many NATO allies are not living up to the commitment they made at their Wales summit meeting in 2014 to spend 2 percent of their gross domestic product on national defense. American presidents have long complained about the lack of burden-sharing by NATO member countries, but Mr. Trump has taken that criticism much further, claiming that some of the United States' closest allies are essentially deadbeats who have failed to pay debts to the organization, a fundamental misunderstanding of how it functions.

The Trump administration has already reportedly been analyzing a large-scale withdrawal of American forces from Germany, after Mr. Trump expressed surprise that 35,000 active-duty troops are stationed there and complained that NATO countries were not contributing enough to the alliance.

In the letter, Mr. Trump told Ms. Merkel that Germany also deserves blame for the failure of other NATO countries to spend enough: "Continued German underspending on defense undermines the security of the alliance and provides validation for other allies that also do not plan to meet their military spending commitments, because others see you as a role model."

In language that is echoed in his letters to the leaders of other countries - including Prime Minister Justin Trudeau of Canada, Prime Minister Erna Solberg of Norway and Prime Minister Charles Michel of Belgium - Mr. Trump said he understands the "domestic political pressure" brought to bear by opponents of boosting military expenditures, noting that he has expended "considerable political capital to increase our own military spending."

"It will, however, become increasingly difficult to justify to American citizens why some countries do not share NATO's collective security burden while American soldiers continue to sacrifice their lives overseas or come home gravely wounded," Mr. Trump wrote to Ms. Merkel.

"As we discussed during your visit in April, there is growing frustration in the United States that some allies have not stepped up as promised," Mr. Trump wrote to Chancellor Angela Merkel of Germany. Clemens Bilan/Epa-Efe, via Rex, via Shutterstock

Mr. Michel reacted tartly last week to the letter, telling reporters at a European Union summit meeting in Brussels that he was "not very impressed" by it, according to a report by Deutsche Welle.

Mr. Trump has long complained about the alliance and routinely grouses that the United States is treated shabbily by multilateral organizations of which it is a member, be it the World Trade Organization or the North Atlantic alliance. But in Europe, the letters to NATO allies have been greeted with some degree of alarm because of their suggestion that Mr. Trump is prepared to impose consequences on the allies - as he has done in an escalating tariff fight with European trading partners - if they do not do what he is asking.

"Trump still seems to think that NATO is like a club that you owe dues to, or some sort of protection racket where the U.S. is doing all the work protecting all these deadbeat Europeans while they're sitting around on vacation, and now he is suggesting there are consequences," said Derek Chollet, a former Defense Department official who is the executive vice president for security and defense policy at the German Marshall Fund of the United States.

"Europeans have been watching Donald Trump begin to implement his rhetoric on trade in ways that are very combative," he said, "and they're starting to contemplate whether he would do this regarding security issues, as well."

Mr. Trump's letter to Mr. Trudeau was reported last month by iPolitics in Canada, and the existence of others was reported last week by Foreign Policy. It was not clear precisely how many Mr. Trump wrote, and the White House would not comment on presidential correspondence. But two diplomatic sources said they believed at least a dozen were sent, including to Italy, Luxembourg, the Netherlands, Portugal and Spain.

A White House official, speaking on the condition of anonymity because the official was not authorized to discuss the matter, said that Mr. Trump is committed to the NATO alliance and expects allies to shoulder "their fair share of our common defense burden, and to do more in areas that most affect them."

John R. Bolton, Mr. Trump's national security adviser, said Sunday that it was NATO members who refused to spend more on defense - not the president - who were responsible for undercutting the alliance.

"The president wants a strong NATO," Mr. Bolton said in an interview on CBS's "Face the Nation." "If you think Russia's a threat, ask yourself this question: Why is Germany spending less than 1.2 percent of its G.N.P.? When people talk about undermining the NATO alliance, you should look at those who are carrying out steps that make NATO less effective militarily."

But for diplomats hoping fervently to avoid another high-profile summit meeting collapse with Mr. Trump as the instigator, the letters were concerning.

"Europeans, like many folks in our Defense Department, think that there are many good things that could come out of this summit if only they can keep it from going off the rails," Mr. Chollet said. "They are hoping to survive without irreparable damage, and so the fact that you have all these storm clouds surrounding NATO and Trump is really worrisome."

Mr. Trump's disparagement of Europe and the alliance has become almost routine, leaving some veteran diplomats aghast. Last week, Jim Melville, the United States ambassador to Estonia, told friends and colleagues that he would resign at the end of this month after more than 30 years in the Foreign Service, in part because of the president's language.

"For the President to say the E.U. was 'set up to take advantage of the United States, to attack our piggy bank,' or that 'NATO is as bad as NAFTA' is not only factually wrong, but proves to me that it's time to go," Mr. Melville wrote in a Facebook post. He was referring to remarks about Europe that the president made during a rally last week in Fargo, N.D., and comments about NATO that he is reported to have made privately during the Group of 7 gathering.

Still, the president is not alone in demanding more robust military spending by NATO allies.

Jim Mattis, the secretary of defense, wrote to Gavin Williamson, the British defense minister, last month saying he was "concerned" that the United Kingdom's military strength was "at risk of erosion" if it did not increase spending, and warned that France could eclipse Britain as the United States' "partner of choice" if it did not invest more. A United States official confirmed the contents of Mr. Mattis's letter, first reported by The Sun.

Correction July 1, 2018

An earlier version of a photo caption with this article misstated the country of which Mark Rutte is the prime minister. It is the Netherlands, not Denmark.

Eric Schmitt contributed reporting.

A version of this article appears in print on July 2, 2018, on Page A1 of the New York edition with the headline: Spend or Else, President Warns NATO Countries.