When President Biden and his aides planned the 75th anniversary of NATO, which opens on Tuesday evening in Washington, it was intended to create an aura of confidence.

The message to President Vladimir V. Putin of Russia and other potential adversaries would be that a larger, more powerful group of Western allies had emerged, after more than two years of war in Ukraine, more dedicated than ever to pushing back on aggression.

But as 38 world leaders began arriving here on Monday, that confidence seems at risk. Even before the summit formally begins, it has been overshadowed by the uncertainty about whether Mr. Biden will remain in the race for a second term, and the looming possibility of the return of former President Donald J. Trump.

Mr. Trump once declared NATO “obsolete,” threatened to exit the alliance and more recently said he would let the Russians do “whatever the hell they want” to any member country he deemed to be insufficiently contributing to the alliance. In recent days, as Mr. Trump has edged up in post-debate polls, key European allies have begun discussing what a second Trump term might mean for the alliance — and whether it could take on Russia without American arms, money and intelligence-gathering at its center.

Mr. Biden will greet the leaders in the vast Andrew W. Mellon Auditorium a few blocks from the White House on Tuesday night — the same room where the treaty creating NATO was signed in 1949, in a ceremony presided over by President Harry S. Truman. Mr. Biden was 6 years old at the time, and the Cold War was in its infancy.

He is now 81 and perhaps the most vocal advocate in Washington for an alliance that has grown from 12 members in 1949 to 32 today as the era of superpower conflict has roared back. But as they gather on Tuesday evening, the leaders will be watching Mr. Biden’s every move and listening to his every word for the same signals Americans are focused on — whether he can go the distance of another four years in office.