The Obama administration warned Russian President Vladimir Putin on Sunday not to react too aggressively to the fast-moving developments in Ukraine, where pro-Western demonstrators forced the nation’s Moscow-backed president from power over the weekend.

National Security Adviser Susan E. Rice said the situation unfolding in Kiev “reflects the will of the Ukrainian people and the interests of the United States and Europe,” and that Russia would be making a “grave mistake” if it sends in military forces to try to reverse the developments — or to seize control of pro-Moscow eastern Ukraine.

The Putin government has shown no outward signs that it is considering such a move. But with Ukraine’s interim government signaling its desire Sunday to quickly put the nation back on course toward Western integration, it was uncertain how far Mr. Putin would be willing to go to save face in a conflict that he had, until recently, appeared to be winning in the former Soviet republic.

Ms. Rice, who appeared Sunday on NBC’s “Meet the Press,” resisted the notion that Moscow and Washington were locked in a kind of Cold War-era standoff over Ukraine. However, other top players in the Obama administration seemed to be working behind the scenes to hammer home a message to Moscow that Washington will not tolerate any Russian aggression in Ukraine.

A Treasury Department official said Sunday night that Secretary Jack Lew spoke by phone with Arseniy Yatsenyuk and told the former economics minister and opposition leader that there was “broad support” at a just-concluded Group of 20 meeting for economic assistance from the U.S. and Europe “as soon as the transitional Ukrainian government is fully established by the parliament.”

In a telephone call Sunday to Russian Foreign Minister Sergey Lavrov, Secretary of State John F. Kerry “underscored the United States’ expectation that Ukraine’s sovereignty, territorial integrity and democratic freedom of choice will be respected by all states,” said one senior State Department official.

Outside the Obama administration, Republican foreign policy heavyweights were eager to make the message more clear, even taunting Moscow by suggesting that the pro-democracy unrest in Ukraine may soon spread to Russia.

“If I was Vladimir Putin today at the end of the Olympics, I’d be a little nervous,” said Sen. John McCain, Arizona Republican. “The people of Russia have watched this transpire, and they’re tired of the crony capitalism and kleptocracy that governs Russia today.”

Mr. McCain, who appeared on “Fox News Sunday,” said the ousting of Ukraine’s president was triggered by citizens who wanted Western-style democracy and insisted that for Russia to respond by splitting the nation along its Eastern and Western divide would be intolerable.

He called on U.S. policymakers to “speak out, to make the message clear to Vladimir Putin that a partition of the country would not be acceptable.”

“The Ukrainian people should determine their own future,” he said. “They want to be Western. … They don’t want to be Eastern.”

The political unrest gripping Ukraine boiled over Saturday after a peace deal between protesters and the Yanukovych government collapsed.

Oleksandr Turchinov, a top opposition figure and speaker of the nation’s parliament, assumed presidential powers Sunday.

Ousted President Viktor Yanukovych’s whereabouts and legitimacy were unclear Sunday afternoon, though there were reports that he had fled Kiev in search of refuge among supporters in eastern Ukraine.

Ukraine’s protest movement was sparked in November, when Mr. Yanukovych shocked the nation’s opposition forces in Kiev by suddenly turning his back on a long-anticipated economic integration agreement with the European Union.

When he then alternatively accepted a $15 billion loan package from Russia, the protests gained steam and its grievances expanded to include corruption, human rights abuses and then calls for Mr. Yanukovych’s resignation.

In Russia, meanwhile, the Putin government appeared willing to support Mr. Yanukovych at any cost, hoping it could count on Ukraine as a key element in a Moscow-backed union of former Soviet states.

But with the Ukrainian president now ousted, it is unclear whether Moscow will come through with the funds it has promised.

There were reports Sunday of a top official in Moscow saying the next tranche of the $15 billion loan package would not be paid until a new government is fully formed in Kiev.

The main protest camp in Kiev was filled Sunday afternoon with dedicated pro-democracy demonstrators setting up tents. Across the country, protesters smashed portraits of Mr. Yanukovych and took down statues of Soviet founder Vladimir Lenin.

It was a stunning reversal of fortune from last week’s bloody protests, when 25 people were killed and nearly 250 injured when heavily armed and Yanukovych-backed authorities cracked down on the camp — a violent turn that seemed only to embolden the protesters.

Mr. Turchinov said in a televised address Sunday that the top priorities of the post-Yanukovych government include “returning to the path of European integration,” Russian news agencies reported.

The parliamentary speaker is a close ally of Yulia Tymoshenko, a former prime minister who was imprisoned by the Yanukovych government in 2011.

Ms. Tymoshenko, who rose as a heroine of Ukraine’s pro-democracy movement during the 2004 Orange Revolution, was freed from prison over the weekend and could emerge as a major player if new elections are held.

Several news organizations reported that the new leadership in Kiev seeks to hold presidential elections May 25.

In Washington, Ms. Rice tried to downplay the idea that the U.S. and Russia have opposing interests in Ukraine.

“This is not about the U.S. and Russia; this is about whether the people of Ukraine have the opportunity to fulfill their aspirations and be democratic and be part of Europe, which they choose to be,” she said.

“It’s in nobody’s interest to see violence returned and the situation escalate,” said Ms. Rice, adding that Ukraine could have “long-standing historic and cultural ties to Russia” while moving to “integrate more closely with Europe.”

“These need not be mutually exclusive,” she said.

• This article is based in part on wire service reports.

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