The White House backs the Ukrainian government's decision to direct its military to confront pro-Russian militants and attempt to retake buildings and other areas they've seized in the eastern part of the country.

The Ukrainian military flooded into an airport near Slovyansk, Ukraine on Tuesday and reportedly retook it with little resistance, although Russian news media reported four fatalities in the vicinity of the airport.

Ukraine's acting president, Oleksandr Turchynov, earlier Tuesday announced an “anti-terrorist operation” against the militants who have seized control of several buildings in cities in eastern Ukraine.

President Obama's spokesman Jay Carney said the U.S. is not providing "lethal assistance" to the Ukrainians and does not see a “military solution” to end the conflict with Russia but supports Kiev's decision to try to preserve "law and order" in the eastern part of the country.

“We understand the government of Ukraine is working to try to calm the situation in the east,” Carney said.

He said the action Ukraine is taking “will be gradual and responsible and [one that] limits violence.”

“The Ukrainian government has a responsibility to provide law and order,” he added. “The best way to deescalate the situation is for the armed militants to leave the buildings that they seized.”

Carney said the U.S. has urged Kiev to maintain restraint. He noted that Ukrainian officials do not consider the use of force the preferred option, but have been placed "in a very difficult situation" by the actions of pro-Russian militants, who have seized building and blocked roads.

U.S. officials remain worried about the possibility of a Russian invasion into Ukraine with thousands of Russian troops amassed at Ukraine's eastern border. In a "frank and firm" call with Russian President Vladimir Putin Monday, Obama urged him to disperse those troops as a way to de-escalate the crisis, Carney said.

U.S., Ukrainian, Russian and European Union officials will meet in Geneva Thursday to consider next steps. European Union officials convened in Luxembourg Monday and decided to impose additional sanctions over Russia's decision to annex the Crimea region of Ukraine.

Carney would not say whether the U.S. would move forward unilaterally with additional sanctions on Russia or whether officials would try to persuade European partners that more sanctions are needed.

This story is based in part on wire reports. The story was first published at 1:19 p.m. and has been updated.