WASHINGTON — The Biden administration warned on Friday that with President Vladimir V. Putin of Russia moving more troops toward the Ukrainian border, a full-scale invasion of Ukraine could start before the end of the Winter Olympics in Beijing, despite speculation that the Russians would wait to invade.

“We continue to see signs of Russian escalation, including new forces arriving at the Ukrainian border,” Jake Sullivan, the president’s national security adviser, told reporters on Friday. Mr. Sullivan said that an invasion could begin “during the Olympics,” which are scheduled to end next week, and warned that all Americans should leave Ukraine in the next 24 to 48 hours.

“We are ready either way,” Mr. Sullivan said. “Whatever happens next, the West is more united than it has been in years.”

U.S. intelligence officials had initially thought Mr. Putin was prepared to wait until the end of the Winter Olympics in Beijing to avoid antagonizing President Xi Jinping of China, a critical ally. In recent days, they say, the timeline began moving up, an acceleration that Biden administration officials began publicly acknowledging on Friday.

Antony J. Blinken, the secretary of state, told reporters at a news conference in Melbourne on Friday that “invasion could begin at any time. And, to be clear, that includes during the Olympics,” which are scheduled to end on Feb. 20. Mr. Blinken added that U.S. officials “continue to see very troubling signs of Russian escalation, including new forces arriving at the Ukrainian border.”

American officials have warned of a grim toll if Mr. Putin proceeds with a military invasion of Ukraine, including the potential deaths of 25,000 to 50,000 civilians, 5,000 to 25,000 members of the Ukrainian military and 3,000 to 10,000 members of the Russian military. On Friday, Mr. Sullivan said that officials believed that an attack would likely start with missile and aerial attacks, and continue with a ground invasion.

“Russia could choose in very short order to commence a major military action against Ukraine,” Mr. Sullivan said, but added that officials could not be sure exactly when, or if, Mr. Putin may decide to invade.