WASHINGTON — President Barack Obama’s national security adviser said Sunday it would be a “grave mistake” for Russia to intervene militarily in Ukraine.

Susan Rice said on NBC television’s “Meet the Press” that in Obama’s phone conversation with Russian President Vladimir Putin on Friday the two agreed that a political settlement in Kiev, the Ukrainian capital, should ensure the unity of the country and the right of Ukrainians to express their free will. She was asked whether the White House fears Putin will send Russian troops into Ukraine.

“That would be a grave mistake,” she said. “It’s not in the interest of Ukraine or of Russia or of Europe or the United States to see the country split.”

Protesters occupied a main square in downtown Kiev late last year after President Viktor Yanukovych abandoned an agreement that would have strengthened his country’s ties with the European Union in favor of seeking closer cooperation with Moscow.

Rice said that in the weeks ahead, Washington will cooperate with Europe and international organizations to help the Ukrainian economy, which she described as fragile.

Speaking on a separate Sunday show, Republican Sen. John McCain, a frequent critic of Obama’s foreign policy, echoed some of the same themes as Rice on seeking to help Ukraine.

He said the United States needs to be clear with Putin that Ukrainians must be allowed to determine their own future and that partitioning the nation would be unacceptable.

“They want to be Western,” McCain said on CBS’s “Face the Nation.” ”That’s what this whole hundreds of thousands in the square was all about. They don’t want to be Eastern.”

McCain said he has spoken with an array of Ukrainians in the opposition movement in recent days. They are overjoyed, McCain said, but they are also worried about the economy.

“Their economic situation is so dire that literally the economy is on the verge of collapse and they’re going to need help immediately,” McCain said.

The White House has urged Ukraine to move swiftly to form a unity government and help restore order after a spate of deadly violence.

Months of protests turned violent last week, with scores killed in clashes between demonstrators and police.

Under a European-mediated plan, protest leaders and Yanukovych agreed Friday to form a new government and hold early elections. Parliament slashed the president’s powers and voted to release his chief rival, former Prime Minister Yulia Tymoshenko, from prison.

By Saturday, protesters had taken over the capital of Kiev and seized the president’s office as parliament voted to remove him and hold new elections. A top opposition figure assumed presidential powers on Sunday. Yanukovych called it a coup and insisted he would not step down, but his whereabouts and grip on power are unclear after he left Kiev for his support base in largely Russian-speaking eastern Ukraine.

In urging calm, White House press secretary Jay Carney said Saturday that the US urged the prompt formation of a broad, technocratic government of national unity.

“We have consistently advocated a de-escalation of violence, constitutional change, a coalition government, and early elections, and today’s developments could move us closer to that goal,” Carney said in a statement. “The unshakeable principle guiding events must be that the people of Ukraine determine their own future.”

The US also welcomed Tymoshenko’s release from a prison hospital.

“We continue to urge an end to violence by all sides and a focus on peaceful, democratic dialogue, working pursuant to Ukraine’s constitution and through its institutions of government,” Carney said, adding that the US will continue to work with its allies, Russia, and European and international organizations “to support a strong, prosperous, unified, and democratic Ukraine.”

Secretary of State John Kerry and Russian Foreign Minister Sergey Lavrov agreed on the need to resolve the situation without violence when they spoke by phone Saturday afternoon, the State Department said in a statement.

Kerry “expressed the importance of encouraging Ukraine to move forward on a path towards constitutional change, de-escalation, the creation of a coalition government, early elections and rejection of violence,” the State Department said in describing the call.

Copyright 2014 The Associated Press.