By Laura Smith-Spark and Phil Black
KHARKIV, Ukraine (CNN) -- An "anti-terrorist operation" is under way in part of Ukraine's eastern Donetsk region, Ukraine's acting President Oleksandr Turchynov told the country's parliament Tuesday.
"It will be conducted step by step, responsibly, cautiously," he said. "The aim of these actions is to protect the citizens of Ukraine, to stop terror, to stop criminality, to stop attempts to tear Ukraine to pieces."
A spokesman for Ukraine's National Security and Defense Council, Evgen Rojenyuk, confirmed that a National Guard battalion made up of 350 troops was sent to eastern Ukraine from Kiev on Tuesday morning.
Rojenyuk said the battalion was headed for the Donetsk region.
The deployment was also confirmed by the deputy head of Ukraine's Internal Affairs Ministry, Mikola Velychkovich, though he would not confirm the numbers involved, where the battalion was headed, or what orders it would be given. He said the ministry would decide on a plan of action once the troops arrive in eastern Ukraine.
Turchynov had given pro-Russian protesters in eastern Ukrainian cities until 2 a.m. ET Monday to disarm or face a "full-scale anti-terrorist operation" by Ukraine's armed forces.
But the deadline passed with no sign that it was heeded, including in the city of Donetsk, where protesters have held the regional government building for more than a week. Similar deadlines in the past have come and gone with no consequences.
A CNN team in Kramatorsk, to the north of the Donetsk region, said police there appeared to have taken back control of a police headquarters building from pro-Russian activists.
However, pro-Russian protesters are still occupying the City Council building in Kramatorsk.
The reported operation comes as EU defense ministers and NATO chief Anders Fogh Rasmussen meet in Luxembourg, with the crisis in Ukraine high on the agenda.
As he arrived for the talks, Rasmussen told reporters he was "deeply concerned" by the latest developments in Ukraine, citing continued violence by small groups of separatists and Russia's continued military pressure on Ukraine's border.
"I call on Russia to de-escalate the crisis, to pull back its troops from Ukraine's borders, to stop destabilizing the situation in Ukraine and make clear that it doesn't support the violent actions of pro-Russian separatists," he said.
"Russia should stop being part of the problem and start being part of the solution."
He said NATO and the European Union are not discussing military options, and that they support a diplomatic and political solution to the crisis.
"However, we are focused militarily on strengthening defense of our allies. That's our core task," he said.
A U.N. human rights report released Tuesday on the situation in Ukraine, including the Crimea region -- which was annexed by Russia last month -- cited an urgent need to counter "misinformation, propaganda and incitement to hatred" in the country to avoid the further escalation of tensions.
"Facts on the ground need to be established to help reduce the risk of radically different narratives being exploited for political ends," said U.N. High Commissioner for Human Rights Navi Pillay.
Based on information gathered by U.N. human rights monitors since March 15, the report draws concerning parallels between what happened in Crimea and events unfolding in eastern Ukraine now.
"In eastern Ukraine, where a large ethnic Russian minority resides, the situation remains particularly tense," the report said. "It will be important to immediately take initial measures to build confidence between the government and the people, and among the various communities, and reassure all people throughout Ukraine that their main concerns will be addressed."
Russia has said it reserves the right to intervene to protect the rights of ethnic Russians in eastern Ukraine.
Far from pulling back Monday in light of the government deadline, protesters forced police officers from their headquarters in the eastern Ukrainian city of Horlivka, witnesses said.
And in Slaviansk, Ukrainian authorities appeared to take no action to retake a police station that was occupied over the weekend. Pro-Russian protesters milled around with makeshift shields outside the building.
When asked why the authorities had made no apparent move to evict protesters after the deadline passed, Ukrainian Deputy Foreign Minister Danylo Lubkivsky told reporters that the government still believes in a political solution.
Although it wants to avoid bloodshed, the government still will protect the country's territorial integrity, he said Monday in Kiev.
Horlivka would be at least the 10th city or town in eastern Ukraine where activists have taken over security or government buildings in recent days.
Obama urges Putin to use influence
Also Monday, U.S. President Barack Obama and Russian President Vladimir Putin spoke about the worsening crisis. The two leaders last spoke March 28.
According to the White House, Obama urged Putin to withdraw Russian troops from Ukraine's border and to use his influence to persuade armed pro-Russian groups to leave the buildings they have seized.
"The President noted Russia's growing political and economic isolation as a result of its actions in Ukraine and made clear that the costs Russia already has incurred will increase if those actions persist," the White House said.
According to a Russian statement, Putin stressed the protests "are the result of the Kiev authorities' unwillingness and inability to take into account the interests of the Russian and Russian-speaking population" and called on Obama to help prevent the use of force.
"In response to the U.S. President's expressed concern about Russia's alleged interference in southeastern Ukraine, the President of Russia noted that such speculations are based on inaccurate information," it read.
European Union foreign ministers on Monday agreed to expand the list of those subject to sanctions and took further steps to help Ukraine economically, as Kiev's interim government seeks closer ties to the West.
"Any further action aimed at destabilizing Ukraine must stop. It is crucial that Russia and Ukraine engage in a meaningful dialogue to find a political solution," said EU foreign policy chief Catherine Ashton.
Pretext for intervention?
The unrest is the latest in a series of events ratcheting up tensions between Ukraine and Russia, which Kiev accuses of fomenting trouble in Russian-speaking eastern Ukraine.
After then-Ukrainian President Viktor Yanukovych backed out of a deal with the European Union in November in favor of closer ties with Russia, he was forced from office in February, the result of months of protests in Kiev.
Distrust among the population in eastern Ukraine, the base of Yanukovych's power, grew as the new national government shifted rapidly in a pro-Western direction. A short time later, pro-Russian elements occupied the Black Sea peninsula of Crimea, which Russia annexed in March. Since then, pro-Russian protesters have taken to the streets in eastern Ukraine and in some cases stormed and occupied buildings.
Kiev's fragile new government and the West accuse Russia of destabilizing the region as a pretext potentially to send in troops to protect the local Russian-speaking population.
NATO says Russian armed forces are massing on Ukraine's eastern border, while Moscow says they are merely carrying out military exercises.
CNN's Phil Black reported from Kharkiv and Laura Smith-Spark wrote and reported in London. CNN's Kellie Morgan, Nick Paton Walsh, Carol Jordan, Larry Register, Richard Roth, Jason Hanna, Marie-Louise Gumuchian and Tim Lister contributed to this report, as did journalist Azad Safarov.
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