Sen. Kelly Ayotte, R-N.H., urged President Obama to "reset the reset" his administration called for with Russia in 2009 to encourage a smooth regime change in Ukraine amidst the roiling situation there.

Ayotte said Obama must take a stronger tack with Russian President Vladimir Putin, who is seen as aiding Ukrainian President Viktor Yanukovych.

"Now that the Olympics are over we need to watch the behavior of the Russians, and 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," Ayotte said on "Fox News Sunday."

Yanukovych fled the capital of Kiev on Saturday as parliament voted him out of office and anti-government protestors and police forces continued to clash. He's described his opponents' actions as a coup d'etat, and said he will not respect parliament's move to oust him.

The White House viewed Saturday's developments as positive, commenting that, "The unshakeable principle guiding events must be that the people of Ukraine determine their own future."

Ayotte said Russia's moves are just as important to watch, as Russia has kept Ukraine close over the years by promising economic benefits — namely through natural gas.

Sen. Dick Durbin, D-Ill., said the United States should be wary of Putin, noting his past as the head of the former Soviet Union's secret police force. But Durbin noted Russia's role as natural gas supplier to Ukraine and others in the region complicates diplomatic efforts to corral Russia.

"The trump card they own is natural gas," Durbin said on "Fox News Sunday."

Yanukovych spurned closer ties with the European Union in November in exchange for discounted natural gas and a multi-billion dollar aid package. That dismayed many Ukrainians who saw the move as continued meddling from Russia, which wants to keep the former Soviet country in its sphere of influence for a discussed economic zone.