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President Obama told Russia's Vladimir Putin on Monday that the U.S. had "grave concern" about Moscow's aggression in Ukraine -- as pro-Russian protesters stormed government buildings in what U.S. officials said appears to be a coordinated effort backed by Moscow.

A senior administration official said the call between the two world leaders was "frank and direct," and was at the request of the Russians.

The White House said Obama told Putin Russia's support of pro-Russia separatists in Ukraine was a matter of "grave concern," and urged Putin to convince the forces to leave the buildings they have seized.

"The president made clear that the diplomatic path was open and our preferred way ahead, but that Russia’s actions are neither consistent with or conducive to that," the official said.

The White House said Obama also told Putin he believes a diplomatic solution cannot succeed as long as the Russian government continues its aggression in Ukraine.

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    The Kremlin also issued a statement about the phone call, saying Putin urged Obama to use the U.S.' capabilities to prevent bloodshed in the region. Putin told Obama that concerns about meddling in southeastern Ukraine are speculations based on "inaccurate information."

    Top Obama administration officials have voiced concern that the latest wave of unrest in eastern Ukraine is strikingly similar to what happened in February and March in the Crimean Peninsula, before the Russian government moved to annex the region.

    The White House said Monday there was "overwhelming evidence" that Russia is behind the new unrest in eastern Ukraine. Amid the tensions, the Pentagon also reported Monday that a Russian jet made several close passes by a U.S. warship in the Black Sea over the weekend.

    U.S. officials suggested they are looking at additional sanctions, but continued to stress that military options, or "lethal aid" for Ukraine, are not being actively considered.

    "We are actively evaluating what is happening in eastern Ukraine, what actions Russia has taken, what transgressions they've engaged in," White House spokesman Jay Carney said. "And we are working with our partners and assessing for ourselves what response we may choose."

    The Obama administration is facing familiar pressure to do more. Sen. John McCain, R-Ariz., said Sunday he wants the U.S. to provide 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.

    In the latest development, a pro-Russian mob on Monday seized a police building in yet another city in Russian-leaning eastern Ukraine, defying government warnings that it was preparing to act against the insurgents.

    Dozens of angry men hurled rocks, smashed the windows and broke into a police station in the city of Horlivka not far from the border with Russia, while hundreds of onlookers cheered them on.

    Pro-Russian gunmen have seized or blocked government buildings in at least nine cities demanding more autonomy from the central government and closer ties with Russia.

    Kiev authorities and Western officials have accused Moscow of instigating the protests, saying the events echoed those in Crimea, which was annexed by Russia last month. Ever since pro-Russian President Viktor Yanukovych fled to Russia in late February, Russia has demanded constitutional reforms that would turn Ukraine into a loose federal state.

    After refusing demands for a referendum by separatists in the east, acting President Oleksandr Turchynov indicated Monday that holding a nationwide referendum on the nation's status was a possibility and that such a vote could be conducted on May 25, along with presidential elections. Turchynov expressed confidence that Ukrainians would vote against turning the country into a federation and against its break-up.

    Meanwhile, a deadline set by the Ukrainian government for pro-Russian gunmen to leave government buildings in eastern Ukraine and surrender weapons passed early Monday, with no immediate sign of any action to force the insurgents out.

    Turchynov had issued a decree Sunday that those protesters who disarm and vacate government offices in several cities in the Russian-leaning east of the country by 0600 GMT Monday will not be prosecuted. Turchynov vowed that a "large-scale anti-terrorist operation" would take place to re-establish control over those areas and that the fate of the Crimean Peninsula, annexed by Russia last month, will not be repeated.

    But Serhiy Taruta, governor of the Donetsk region, where government buildings in several cities, including the regional capital Donetsk, have been seized by pro-Russian gunmen, said an "anti-terrorist operation" was under way in the region, according to the Interfax news agency.

    Taruta did not give any details of what the operation would entail. The governor usually does not have authority to launch such measures on his own and he was likely acting on the orders of top security officials in Kiev.

    Late Sunday, the U.S. 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 composed exclusively of Ukrainian citizens acting of their own volition.

    The Associated Press contributed to this report.