Ukraine's president says a full-scale operation involving the army will be launched in the east after pro-Russian militants seized government buildings.
Acting President Oleksandr Turchynov said he would not allow a repetition of what happened in Crimea which was annexed by Russia last month.
His live televised address from parliament came after pro-Russian forces targeted half a dozen cities.
An urgent meeting of the UN Security Council is under way in New York.
The meeting was called for by Moscow, which has strongly criticised Kiev's plan to use its armed forces in eastern Ukraine.
Earlier, Nato's secretary general voiced concern at events in the region.
And the US ambassador to the UN said the attacks this weekend bore the "tell-tale signs of Moscow's involvement." But the Kremlin denies involvement in events in eastern Ukraine.
Eastern Ukraine has a large Russian-speaking population and has seen a series of protests since the ousting of Ukraine's pro-Russian President Viktor Yanukovych in February.
"We will not allow Russia to repeat the Crimean scenario in the eastern regions of Ukraine," said President Turchynov.
"The aggressor... is continuing to sow disorder in the east of the country."
But Mr Turchynov offered not to prosecute militants who gave up their weapons by early Monday.
According to a Ukrainian presidential decree, pro-Russian separatists should give up their weapons and leave buildings they have occupied by 0600GMT, Reuters reported.
Responding to Mr Turchynov's address, a Russian foreign ministry spokesman said the plan to use the armed forces was "criminal" and caused "particular indignation".
Ukraine was, the spokesman said, "waging war against its own people".
Nato chief Anders Fogh Rasmussen's statement on Sunday drew parallels with some aspects of last month's seizure of Crimea.
He said the "reappearance of men with specialised Russian weapons and identical uniforms without insignia, as previously worn by Russian troops during Russia's illegal and illegitimate seizure of Crimea, is a grave development".
A Nato source told the BBC the organisation believed that "Russian forces have been involved in the seizure of some of the buildings".
And the US ambassador to the UN said the attacks on police and other buildings in eastern Ukraine had "telltale signs of Moscow's involvement".
"It's professional, co-ordinated. Nothing grass-roots about it," ambassador Samantha Power told ABC News.
"The forces are doing in each of the six or seven cities they have been active in exactly the same thing."
A senior Ukrainian intelligence official said his country's special services had evidence proving Russia's direct involvement in the events in eastern Ukraine.
"We have not only evidence, we have 18 detainees, we have career officers of the Main Intelligence Directorate of the Russian Armed Forces, we have arrested agents complete with instructions, arms and explosives," Security Service head Valentyn Nalyvaychenko said in a live TV discussion programme.
On Saturday, armed men took over police stations and official buildings in Sloviansk, Kramatorsk and Druzhkivka.
Similar accounts emerged of armed men dressed in camouflage arriving in buses in Sloviansk and Kramatorsk and storming the police stations.
BBC reporters in Sloviansk said the gunmen were well-organised and quickly established control throughout the town. Checkpoints had been set up on the main roads into the town.
In other developments:
- Rival rallies turned violent in the eastern city of Kharkiv - Ukraine's second biggest - with reports of 10 people injured
- Pro-Russian activists wielding clubs surround Kharkiv's city council, with mayor Henadiy Kernes reportedly inside
- Unconfirmed reports suggested official buildings had also been taken over in two other cities - Mariupol and Yenakievo.
- Pro-Russian demonstrators continued occupying the main administrative building in the regional capital Donetsk, which they have held for one week
- A protest leader told the BBC that the activists in Sloviansk took action to support the Donetsk sit-in.
Early on Sunday Ukrainian authorities said they launched an "anti-terror operation" after armed men took over the city of Sloviansk.
A Ukrainian officer was killed in a gun battle in the city, and there are reports the Ukrainian operation has been halted.
But both sides suffered a number of casualties, interim Ukrainian Interior Minister Arsen Avakov said.
He later said Ukrainian forces had been attacked at a checkpoint on the way to Sloviansk, and at least one officer had been killed and five others wounded. An unknown number of militants were also wounded.
Witnesses at Sloviansk police station said there was no sign yet of any clashes, and the centre of the town was quiet.
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