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.