WASHINGTON—U.S. national security adviser Jake Sullivan on Sunday renewed the Biden administration’s warnings of a possibly imminent Russian invasion of Ukraine as Russia continued to insist it has no such plans and European leaders embarked on further diplomatic attempts to ward off military conflict.

“I can’t get in the head of Vladimir Putin, and I can’t predict exactly what he’s going to do,” Mr. Sullivan said on CBS’s “Face the Nation,” speaking a day after a one-hour phone call between the Russian and U.S. presidents...

WASHINGTON—U.S. national security adviser Jake Sullivan on Sunday renewed the Biden administration’s warnings of a possibly imminent Russian invasion of Ukraine as Russia continued to insist it has no such plans and European leaders embarked on further diplomatic attempts to ward off military conflict.

“I can’t get in the head of Vladimir Putin, and I can’t predict exactly what he’s going to do,” Mr. Sullivan said on CBS’s “Face the Nation,” speaking a day after a one-hour phone call between the Russian and U.S. presidents yielded what senior administration officials said was no fundamental change in the situation. President Biden and Ukrainian President Volodymyr Zelensky were set to speak on the phone Sunday.

“All we can do at President Biden’s direction is prepare—prepare for diplomacy to find a way forward that is sustainable and durable and advances the security of all the United States, Russia and Europe, and prepare for the potential of a major military action in the coming days,” Mr. Sullivan said.

Mr. Sullivan also reiterated calls for any Americans still in Ukraine to “move out by air or rail or road as rapidly as possible.” Seeking to dispel any notion that there would be U.S. military action to extract anyone in the case of Russian action, Mr. Sullivan said there was a “big difference” between the U.S. deployment of thousands of soldiers to Afghanistan last summer to end a 20-year U.S. presence there and its current effort to prevent a war in Ukraine.

“An assault on Ukraine is an assault on democracy,” said House Speaker Nancy Pelosi (D., Calif.) on “This Week With George Stephanopoulos,” saying the U.S. and its allies have sent a clear message to Mr. Putin that “there are very severe consequences to his aggression and that we are united in using them.”

Sen. Lindsey Graham (R., S.C.) has said that the Biden administration needs to clearly spell out consequences if Russia invades Ukraine.

Photo: J. Scott Applewhite/Associated Press

Sen. Lindsey Graham (R., S.C.) criticized the administration’s approach in an interview with Mr. Stephanopoulos. saying, “They’re telling us the invasion is imminent. But they’re not telling Putin with clarity what happens if you invade.”

“The guy took the Crimea in 2014,” Mr. Graham said. “He’s got 100,000 troops amassed on the Ukrainian border, and he’s paying no price at all. So I’d like to hit him now for the provocation and have sanctions spelled out very clearly, what happens to the ruble and his oil and gas economy. I think that’s what’s missing.”

Pentagon press secretary John Kirby, speaking on “Fox News Sunday,” said such pre-emptive measures would be counterproductive. “If you punish somebody for something that they haven’t done yet then you might as well just go ahead and do it. So we believe there’s a deterrent effect by keeping them in reserve,” he said. “Right now we are not considering a pre-emptive sanction regime.”

German Chancellor Olaf Scholz, who has tried to balance his country’s membership of the Western alliance with its close ties to Russia, is scheduled to meet Mr. Zelensky in Kyiv on Monday and Mr. Putin in Moscow on Tuesday. Earlier this month Mr. Biden pushed the German leader to support tough sanctions on Russia should Moscow invade its smaller neighbor, including closing Nord Stream 2, a recently completed pipeline that is awaiting certification to start pumping natural gas from Russia to Germany. Mr. Scholz on Sunday warned Mr. Putin of “hard reactions” in the event of a Ukraine invasion but hasn’t explicitly put Nord Stream 2 in play.

Mr. Scholz’s trip east follows one by French President Emmanuel Macron,

who recently traveled to Moscow for talks and spoke Saturday with Mr. Putin, telling the Russian leader that sincere dialogue was incompatible with an escalation, according to Mr. Macron’s office.

Meanwhile Poland’s government is preparing for the possibility that a large number of Ukrainian refugees would cross its border in the event of a war, Interior Minister Mariusz Kaminski said Sunday. Officials in the province of metropolitan Warsaw, the capital, were looking at hotels, hostels, schools, churches and other public and commercial buildings that could house a sudden influx.

Just months ago, Poland began building a wall along its eastern border with Belarus to keep mostly Middle Eastern asylum seekers from entering Polish territory. In contrast, Poland’s conservative government has long voiced its willingness to keep taking in large numbers of Ukrainians, whose language is close to Polish. For years, Poland has been a top destination for Ukrainian emigrants and refugees.

—Drew Hinshaw contributed to this article.

Write to Andrew Duehren at andrew.duehren@wsj.com and Gwynn Guilford at gwynn.guilford@wsj.com