As NATO leaders gathered in Washington this week, one American president hailed the 75-year defensive alliance as the greatest “in the history of the world.”

Another described it as a virtual protection racket and declared that he would abandon “delinquent” members to the mercies of Russian invaders.

President Biden was the official host, greeting his European and North American counterparts in Washington with smiles, handshakes and solidarity, posing for grip-and-grin pictures and boasting of the progress and principle underlying the historic partnership. Former President Donald J. Trump was nowhere to be seen, not part of the formal events, but adding his voice from afar at a rally and in an interview.

“The fact that NATO remains the bulwark of global security did not happen by accident,” Mr. Biden said at an opening ceremony in the Andrew W. Mellon Auditorium, where the North Atlantic Treaty was signed in 1949. “It wasn’t inevitable. Again and again, at critical moments, we chose unity over disunion, progress over retreat, freedom over tyranny and hope over fear. Again and again, we stood behind our shared vision of a peaceful and prosperous trans-Atlantic community.”

Just two hours after Mr. Biden finished, Mr. Trump took the stage at a campaign event in Doral, Fla., and denigrated the alliance. He made no mention of its contributions to history, its victory in the Cold War or its role in defending Europe today as the war in Ukraine continues. Indeed, he acknowledged that he had been largely ignorant about the organization until he became president. But he then boasted about how he berated the allies as deadbeats.

“I didn’t know what the hell NATO was too much before,” Mr. Trump told cheering supporters. “But it didn’t take me long to figure it out, like about two minutes. And the first thing I figured out was they were not paying. We were paying, we were paying almost fully for NATO. And I said that’s unfair.”

He went on to repeat a story that he told in February to the shock of world leaders, claiming that as president he had warned his NATO counterparts that he would not defend them if they did not increase their own military spending. “‘Would you protect us?’” Mr. Trump quoted another leader whose country did not meet the spending target as saying. “I said, ‘No, I will not protect you from Russia.’”

Every recent American president has pressed NATO allies to spend more on their own armed forces, but Mr. Trump is the only one who has ever threatened to let them be attacked by Russia. The notion that the United States would abrogate its mutual defense obligations under Article V of the NATO treaty has roiled the alliance.

During his term in the White House, Mr. Trump came close more than once to pulling the United States out of NATO altogether, only to be talked out of it by his advisers. But if he is elected again, he will not have the same advisers around him. He may not need to even formally withdraw to effectively gut the alliance since Article V would no longer be viewed as inviolate.

“President Trump even to this day does not understand that NATO is an alliance among democracies that believes in values,” said Michael McFaul, the director of the Freeman Spogli Institute for International Studies at Stanford University and a former U.S. ambassador to Russia. “It’s not a protection racket. They don’t pay us to protect them.”

Indeed, as he has done repeatedly over the years, Mr. Trump distorted how NATO works, making it sound as if the allies were supposed to pay the United States. In fact, at issue has been how much each member is to spend on its own military. And while his browbeating may have been one reason some members did increase their investments during his tenure, he overstated how much progress was made.

Mr. Biden, by contrast, has overseen a far greater increase in spending by NATO members. That, of course, may owe less to either American president than it does to President Vladimir V. Putin of Russia and the 2022 invasion of Ukraine that terrified European allies. But many European officials credit Mr. Biden with strengthening the alliance, which had frayed under Mr. Trump.

In Mr. Trump’s last year in office, just nine NATO members were meeting the target of spending 2 percent of their national economies on their armed forces ahead of a 2024 goal. Since Mr. Biden took over, that number has grown to 23. Mr. Biden likewise presided over the addition of two important new members to NATO, Sweden and Finland, bringing the alliance to 32 members.

“It’s remarkable progress,” Mr. Biden said, “proof that our commitment is broad and deep, that we’re ready, that we’re willing and we’re able to deter aggression and defend every inch of NATO territory across every domain: land, air, sea, cyber and space.”

Mr. Trump, predictably, sought to claim credit for anything good that happened on Mr. Biden’s watch. “I took in the money that he’s spending right now,” Mr. Trump told the Fox News host Brian Kilmeade on his radio show. “If I didn’t take it in, they wouldn’t even have a NATO to fight Russia. It was me that took in all the money.”

Unlike Mr. Biden’s vows to continue aid for Ukraine, Mr. Trump offered no such words of support. Instead, while NATO leaders in Washington condemned Mr. Putin for his unprovoked war, which included an attack this week on a children’s hospital, Mr. Trump remarked on his close friendship with the Russian leader.

“You wouldn’t have had Ukraine attacked if I were president,” Mr. Trump told Mr. Kilmeade, a counterfactual view shared by few, if any, Russia experts who are not political supporters of Mr. Trump. “You wouldn’t have had it. I had a very good relationship with President Putin. We get along very well.”

Even as Mr. Biden was conducting diplomacy, his campaign used the summit to attack Mr. Trump for that “very good relationship” with the Russian president. In a new online ad, the Biden campaign said that Mr. Trump would “walk away from NATO” and “gave Putin a green light to attack whoever he wants.” It concluded: “Because this is who Donald Trump is — a lap dog for a dictator who blames America first.”

While Mr. Trump did not attend the meetings in Washington, he planned to host one of the NATO leaders afterward. Prime Minister Viktor Orban of Hungary, whose authoritarian leadership has made him an outlier in Europe, was expected to fly to Florida after the alliance meeting for a visit with Mr. Trump.

But with the exception of Mr. Orban, experts and officials said, the presidents and prime ministers gathered for the anniversary were dreading the possibility that he might win again.

“You cannot get five minutes into a conversation that doesn’t turn to the future of who’s going to be the next president,” Mr. McFaul said. “There’s a lot of anxiety right now within the NATO alliance about what happens if Mr. Trump is re-elected.”