COLORADO SPRINGS, Colorado, June 1 (Reuters) - U.S. President Joe Biden predicted on Thursday Sweden will join NATO "soon", speaking at the U.S. Air Force Academy days after he hinted at a possible deal to overcome Turkey's opposition to admitting the Nordic country to the alliance.

Biden, in a flag-waving commencement address in Colorado Springs, Colorado, warned graduates they will enter service in an increasingly unstable world, citing challenges from Russia and China.

Biden, 80, who stood for much of the hours-long ceremony to shake hands with graduates, appeared to trip over something and fell to his knees towards the end. He was assisted to his feet and walked to his seat unaided.

On Monday, Biden spoke to Turkish President Recep Tayyip Erdogan to congratulate him on his re-election. Biden told reporters Erdogan repeated Ankara's desire to buy F-16 fighter jets from the United States, while Biden urged Ankara to drop its objection to Sweden's joining NATO.

In his commencement speech, Biden said NATO is stronger in spite of Russian President Vladimir Putin's attempt to crack the alliance with his invasion of Ukraine. It is bolstered further, he said, by the recent admission of Finland, "and soon, Sweden."

"It will happen, I promise you," he said, but provided no details.

On Monday, Biden said he would speak to Erdogan again soon. NATO's annual summit is in Vilnius, Lithuania, in July.

On Tuesday, U.S. Secretary of State Antony Blinken urged Turkey to immediately finalize Sweden's accession to NATO, saying the country had already taken significant steps to address Ankara's objections to its membership.

The White House has denied that Biden is pursuing a deal with Turkey to lift its opposition in exchange for F16s.

The 80-year-old president, who is seeking re-election in 2024, stood, throughout the presentation of more than 900 diplomas despite the relatively thin mountain air, shook hands and gave sharp salutes to the blue-uniformed graduates. His fall came at the end of the individual salutes. The Air Force Academy stands at 7,258 feet (2,212.3 meters) above sea level.

Biden made clear the United States would not back down from the challenge posed by China amid deep strains in the relationship.

"The United States does not seek conflict or confrontation with China. China and the United States should be able to work together where we can to solve some global challenges, like climate," he said.

"But we are prepared for vigorous competition," he said, adding the United States would stand up for its interests and that of its partners.

The president emphasized U.S. support for Ukraine in the war with Russia.

"The American people's support for Ukraine will not waver," Biden said.