Updated

The Obama administration and a top Senate Republican agreed Sunday that the Russian government appears behind the recent uprising in eastern Ukraine but remain split on the level of U.S. response.

"It's professional, it's coordinated,” Samantha Power, the U.S. ambassador to the United Nations, told ABC’s “This Week.” “There's nothing grassroots-seeming about it."

She also said the violence bears the “tell-tale signs of Moscow involvement” and that tougher penalties on Russia could follow if the aggression continues.

Arizona GOP Sen. John McCain wants the United States to instead take a more hawkish approach to keeping Russian forces from moving deeper into Ukraine, after Russia last month annexed the country’s bordering Crimea region. He wants the U.S. to provide more arms to the Ukrainians and impose additional and “severe” sanctions on the Russian economy.

"We ought to at least, for God's sake, give them some light weapons with which to defend themselves,” he told CBS’ “Face the Nation.

McCain also suggested the administration is withholding intelligence from the Ukrainian government and put much of the blame on President Obama and Secretary of State John Kerry.

"Where is the president of the United States?” McCain asked. “Shouldn't the president of the United States be speaking forcefully and strongly? And didn't the president say if they carried out further actions, there would be further sanctions? So far, we haven't heard anything."

Ukrainian officials said Sunday a Security Service officer was killed in an exchange of gunfire with a pro-Russian militia in the eastern city of Slovyansk, where the police station and the Security Service office were seized Saturday by armed men.

Since Russian forces took control of Crimea, amid months of political turmoil in Ukraine, the unrest has spread to several cities in the country’s eastern region, including the major industrial city of Donetsk.

Late Sunday, the State Department issued a statement titled: "Russian Fiction: The Sequel, 10 More False Claims about Ukraine."

The document was intended to be a followup to Obama saying last month: "No amount of propaganda can make right something that the world knows is wrong.”

The document in part states Russia falsely claims its agents are not in the Ukraine and that the pro-Russia demonstrations are comprised exclusively of Ukrainian citizens acting of their own volition.

Kerry recently spoke by phone with Russian Foreign Minister Sergey Lavrov, expressing his "strong concern" that the attacks in eastern Ukraine were "orchestrated and synchronized, similar to previous attacks in eastern Ukraine and Crimea," according to the State Department.

The agency also said Kerry vowed additional consequences should Russia fail to take steps to de-escalate and move troops back from Ukraine's border.

Russia's Foreign Ministry is denying Kerry's claims. It says the crisis in Ukraine was caused by the failure of Ukraine's government to consider "the legitimate needs and interests" of the Russian-speaking population in Slovyansk and elsewhere in the country.

McCain, who keeps in close contact with Ukraine’s provisional government, told CBS the U.S. and Europe should impose "severe penalties” or sanctions that will have an impact on the Russian economy.

He called Russian President Vladimir Putin’s actions  “predictable” and suggested the uncheck unrest he is creating is destabilized the Ukraine government, established after its pro-Moscow president was ousted in February.

"Right now [Putin] is going full speed ahead down the freeway,” McCain said. “And there's no tangible evidence of him having to pay a significant penalty."

The Associated Press contributed to this report.