WASHINGTON — President Obama’s national security adviser warned Russian President Vladimir Putin that it “would be a grave mistake” to send troops into Ukraine.

“It’s not in the interests of Ukraine or of Russia or of Europe or the United States to see a country split,” National Security Adviser Susan Rice said Sunday on NBC’s “Meet the Press.”

“It’s in nobody’s interests to see violence return and the situation escalate.”

The upheaval threatened to unravel the country of 46 million, which is divided into pro-European Union and pro-Russia factions.

The tensions were exasperated by Ukraine’s dismal economy and alleged corruption of President Viktor Yanukovych, who was forced out of office.

Despite the stern warning for Moscow, Rice insisted Ukraine’s political upheaval wasn’t reviving the Cold War rivalry between the United States and Russia.

“That’s a pretty dated perspective that doesn’t reflect where the people of Ukraine are coming from,” she said. “This is not about the US 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.”

Obama told Putin in a phone call that the United States and Russia have a shared interest in keeping Ukraine unified and independent, Rice said.

“There is not an inherent contradiction between a Ukraine that has long-standing historic and cultural ties to Russia, and a modern Ukraine that wants to integrate more closely with Europe,” she said — pledging that the United States remained “on the side of the Ukrainian people.

But Sen. John McCain (R-Ariz.) told CBS’s “Face the Nation” that Putin should be “nervous” about Ukraine’s turn toward Europe.

“They want to be Western. They don’t want to be Eastern,” he said. “If I were Vladimir Putin, I would be a little bit nervous.”

Ukraine’s political landscape changed dramatically Saturday following a violent crackdown on months-long protests in Kiev that left 82 dead, prompting police, military and lawmakers to turn on President Viktor Yanukovych. Parliament voted Saturday to oust him and to free jailed opposition leader Yulia Tymoshenko.

Lawmakers Sunday voted for an acting president

to replace Yanukovych, who fled the capital but was blocked from leaving the country.

“He’s lost enormous legitimacy — despite having been originally democratically elected — by turning on his people, by using violence in the streets against peaceful protesters, and by flouting the will of the Ukrainian people,” Rice said of Yanukovych.