Top Senate Republicans on Sunday told President Obama to send a “clear” message to Russia President Vladimir Putin to stay out of Ukraine’s political crisis, renewing criticism about the president’s foreign policy and his negotiations with the powerful Russian leader.

“I believe the president needs to up his game and send a clear unequivocal public message to Putin not to interfere in what is happening in Ukraine,” Sen. Kelly Ayotte, R-N.H., a member of the Senate Armed Services Committee, told “Fox News Sunday.” “This is an opportunity for the president to really be unequivocal with Putin right now.”

The months of political upheaval in Ukraine have divided some residents between aligning with Russia or Western nations, a situation now being portrayed as a de facto power struggle between Obama and Putin, who appear on opposite sides of several world issues, including the Syria crisis.

Obama vowed in June 2010 to “reset” relations with Russia in an effort to help solve international problems and improve the world economy. But four years later, little appears to have improved.

"It's time to reset the reset,” Ayotte said.

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Critics of the Obama administration's foreign policy say Putin has had the upper hand in efforts to end Syria’s 3-year-long civil war because Russia is a major ally of Syrian President Bashar Assad, which has allowed him to remain in power and keep a large part of his chemical weapons cache.

Such critics are also bristling over Putin allowing former NSA contractor Edward Snowden, who leaked U.S. government secrets, to live in Russia.

Still, Obama said the situation in Ukraine is about residents being able to make decisions for themselves and not about “some Cold War chessboard."

Susan Rice, Obama's national security adviser, told NBC's "Meet the Press" that the president talked Friday with Putin and that they 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.

This weekend, the Ukraine parliament declared President Yanukovych unable to carry out constitutional duties.

The country's western regions, angered by corruption in Yanukovych's government, want to be closer to the European Union and have rejected Yanukovych's authority in many cities. Eastern Ukraine, which accounts for the bulk of the nation's economic output, favors closer ties with Russia and has largely supported Yanukovych.

The protest movement was prompted by the president's decision to abort an economical agreement with the EU in favor of a deal with Moscow.

Arizona Republican Sen. John McCain, a frequent critic of Obama's foreign policy, 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," he said on CBS' "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 also said an array of Ukrainians in the opposition movement are overjoyed but worried about the economy. And he suggested Putin should be “a little nervous” now that the Olympics are over and his residents -- “tired of crony capitalism” -- might follow neighboring Ukrainians.

Sen. Dick Durbin, D-Ind., the No. 2 Democrat in the Senate, defended Obama, saying he, like every new U.S. president, has tried to negotiate with Putin, who has been a threat for many decades.

He also told “Fox News” the administration will have a challenging time in Ukraine because Russia has the “trump card” of supplying the country with natural gas.

The Associated Press contributed to this report.