Four people were killed Tuesday in clashes between Ukraine's military and pro-Russian armed separatists in the eastern Ukrainian region of Donetsk, Russian state television reported.

Tensions between Russia and Ukraine entered a potentially dangerous new phase, with authorities in Kiev launching an "anti-terror" operation to root out the separatists.

The deaths occurred as the military was retaking control of a small airport near the town of Kramatorsk, acting Ukrainian President Oleksandr Turchynov told parliament.

There was no official confirmation of the death toll. A spokesperson for the separatists said one of their ranks had been wounded in the crossfire.

The interim government in Kiev said earlier that it was deploying troops to northern Donetsk, a region which borders Russia.

"The goal is to protect citizens from terrorists who are trying to tear this country apart," Turchynov said.

The insurgents, who are demanding broader autonomy from Kiev and closer ties to Russia, continued occupying government, police and other administrative buildings in eastern cities, in defiance of Turchynov's ultimatum to lay down their weapons.

A spokesman for the separatists confirmed that government forces had opened fire on pro-Russian activists in the eastern city of Sloviansk, causing several injuries, and said the so-called "self-defence forces" were preparing for a wider attack.

White House spokesman Jay Carney called the escalating situation "very dangerous" and charged that Russia had both "directly and indirectly" precipitated the crisis.

"The Ukrainian government has a responsibility to provide law and order, and these provocations in eastern Ukraine are creating a situation in which the government has to respond," Carney said.

Measures to curb the activities of what the Kiev leadership are referring to as "terrorists" were met with outrage in Moscow.

Russian President Vladimir Putin called Ukraine's military operations "unconstitutional," during a phone call with UN Secretary General Ban Ki-moon, the Kremlin said.

Putin told Ban that the military operations against separatists would only escalate the crisis, and he urged the United Nations and the West to condemn Kiev's actions.

In Beijing, Russian Foreign Minister Sergei Lavrov said that any move against pro-Russian protesters by the Ukrainian government would undermine four-party talks set for Thursday in Geneva.

Lavrov denied that Russia was seeking to undermine the talks between Ukraine, Russia, the United States and the European Union, Russia's Interfax news agency quoted him as saying. He said allegations that Russia was organizing anti-government protests in south-eastern Ukraine were "nonsense."

In Washington, the United States said new rounds of sanctions would wait at least until after Thursday's meeting.

State Department spokeswoman Jen Psaki said the US does anticipate additional sanctions aimed at Russians and Ukrainians who have supported pro-Russian separatism, in coordination with the EU.

If Russia invades eastern Ukraine, "that unfortunate step" would "certainly" prompt serious consideration of sanctions against key economic sectors, Psaki said, noting that broader sanctions could be deployed even without an invasion.

In Estonia, US Senator John McCain urged the US government to supply weapons to the Ukrainian government.

"They do not even have defensive armour. ... They do not have so much equipment that they are badly in need of," he said in Tallinn. "And for us not to do that is absolutely inexcusable and shameful behaviour, and I am embarrassed that we do not give them what they need to defend their country."

In Luxemburg, NATO Secretary General Anders Fogh Rasmussen discussed with EU defence ministers the implications of the Ukraine crisis for European security.

There was consensus that it was time for EU and NATO countries to "get real" on defence spending, said Maciej Popowski, deputy secretary general of the European External Action Service.

Dwindling defence budgets have been a concern in Europe since the region's economic crisis.

Popowski argued that events in Ukraine should act as "a trigger" for more defence spending and cooperation.

Rasmussen confirmed there are no plans for military intervention in Ukraine, arguing that "the right way forward is to find a political and diplomatic solution."