WASHINGTON (AP) — President Joe Biden wants Ukraine to win the war against Russia. But he doesn't want World War III — especially with nuclear weapons.

Balancing those two goals has been difficult, and the tension was on particular display at the NATO summit in Vilnius this week.

Ukrainian President Volodymyr Zelenskyy made an emotional, even caustic, demand for a clear path toward joining the alliance.

But Biden, who was to try to showcase NATO's strength in a sum-up speech Wednesday evening, was not willing to take that step, even as the United States continues to provide more weapons and ammunition than any other country to Ukraine.

The competing priorities in the midst of Europe's bloodiest war in generations created an undercurrent of friction even as Biden and Zelenskyy projected a united front during their meeting as the summit drew to a close.

The public encounter had the vibe of two leaders clearing the air, and each conspicuously heaped praise on his counterpart.

Biden lauded Zelenskyy and Ukrainians for their courage by saying it's "been a model for the whole world to see." Zelenskyy thanked Biden and the American people for billions of dollars in military assistance, saying that "you spend this money for our lives."

Wearing a blue-and-yellow-striped tie in the colors of the Ukrainian flag, Biden acknowledged that Zelenskyy has occasionally been unsatisfied by unfulfilled requests for weapons.

"The frustration, I can only imagine," Biden said. "I know that you're many times frustrated about whether things get to you quickly enough, what's getting to you and how we're getting it. But I promise you, the United States is doing everything we can to get you what you need."

Biden also said the war had created a sense of unity about opposing international aggression.

"It's bringing the world together," he said. "It's a hell of a price to pay, but it's bringing the world together."

The meeting came after a few other encounters between Biden and Zelenskyy at the summit. They sat close to each other at the inaugural meeting of the NATO-Ukraine Council, a new forum that's intended to give Kyiv a greater voice within the alliance.

And they shared the stage as the Group of Seven, which includes the world's most powerful democratic countries, announced plans for long-term security assistance for Ukraine.

But Wednesday afternoon was the first opportunity for Biden and Zelenskyy to sit down privately with their advisers — after their public comments.

And by then, Zelenskyy had softened his tone considerably. En route to Vilnius on Tuesday, he had blasted NATO's vague plans for Ukraine's eventual membership, tweeting, "It's unprecedented and absurd when a time frame is set neither for the invitation nor for Ukraine's membership."

Jake Sullivan, Biden's national security adviser, said everyone "needs to look squarely at the fact" that allowing Ukraine to join NATO at this point "means war with Russia."

"That is an inescapable fact," he told CNN.

Sullivan credited Biden with ensuring that NATO is "more unified and more determined and more decisive than at any point."

"That's President Biden's legacy when it comes to NATO, and it's one that he can be very proud of," he said.

In an interview with The Associated Press before Biden left on his trip, Senate Minority Leader Mitch McConnell said the president has been "heading in the right direction but not fast enough" when it comes to supporting Ukraine.

"The weapons transfers never seem to happen as soon as they're announced," said McConnell, a Kentucky Republican. Although Ukrainians are "extremely grateful for the help," he said, the assistance "frequently doesn't get there soon enough to be the most effective."

Although McConnell has been a firm supporter of sending help to Ukraine, other Republicans have voiced skepticism, creating uncertainty about Biden's ability to make long-term financial commitments.