Pro-Russian protesters who seized the regional government building in the Ukrainian city of Donetsk are reported to have declared a “people’s republic”.
The rebels have called for a referendum on secession from Ukraine by 11 May.
Ukrainian security officials are being sent to the eastern cities of Donetsk, Luhansk and Kharkiv after pro-Russia groups occupied government buildings.
Interim President Oleksandr Turchynov called the unrest an attempt by Russia to “dismember” Ukraine.
In an address on national TV, he said it was “the second wave” of a Russian operation to destabilise Ukraine, overthrow the government and disrupt planned elections.
Russia recently annexed Ukraine’s Crimean peninsula after a referendum there which Ukraine did not see as valid.
As tensions mounted on Monday, Ukrainian Foreign Minister Andriy Deshchytsya told Russia’s Ekho Moskvy news agency that Kiev would go to war with Russia if it sent troops into eastern Ukraine.
Moscow has thousands of troops massed along its border with Ukraine. It says it has no intention of invading but reserves the right to protect the rights of ethnic Russians.
Protesters broke into Donetsk’s regional government building and another in Kharkiv – Ukraine’s second largest city – on Sunday. Ukrainian authorities say protesters have now left the building in Kharkiv.
Ukrainian news agency Unian says gunmen also tried to storm a Donetsk TV building on Monday but were deterred by police.
At an emergency cabinet meeting, interim Prime Minister Arseniy Yatsenyuk blamed Russia for the seizures.
“The plan is to destabilise the situation, the plan is for foreign troops to cross the border and seize the country’s territory, which we will not allow,” he said, adding that people engaged in the unrest had distinct Russian accents.
He said Russian troops remain within 30km (19 miles) of the frontier. The city of Luhansk is just 25km from the Russian border.
Police have blocked roads into Luhansk and armed reinforcements are being sent to the restive cities.
Officials said Ukrainian National Security Secretary Andriy Parubiy and Security Service chief Valentyn Nalyvaychenko have been sent to the city.
Interior Minister Arsen Avakov has already arrived in Kharkiv and First Deputy Prime Minister Vitaly Yarema is on his way to Donetsk, a spokeswoman said.
She said the three officials had “all the authority necessary to take action against separatism.”
President Turchynov has cancelled a visit to Lithuania to deal with the unfolding events.
Russia’s foreign ministry said it was “closely watching” events in eastern Ukraine, “particularly in Donetsk, Luhansk and Kharkiv regions”.
It reiterated Moscow’s demands for the creation of a federal Ukraine with broader powers for provinces.
“Stop pointing to Russia, blaming it for all of the troubles of today’s Ukraine,” the statement said.
The crisis has heightened nervousness in many other eastern European states, with Czech President Milos Zeman saying Nato should deploy troops in Ukraine if Russia invades.
“If Russia decides to extend its territorial expansion to eastern Ukraine, the fun is over,” he told Czech public radio on Sunday.
In another development on Monday, Nato said it was limiting Russian diplomats’ access to its headquarters in Brussels.
It comes days after Nato foreign ministers agreed to suspend all practical co-operation with Moscow over its annexation of Crimea.
The latest developments come as Ukraine’s defence ministry said a Russian soldier had killed a Ukrainian military officer still loyal to Kiev in eastern Crimea late on Sunday.
The circumstances are unclear. Russian news agencies said prosecutors had opened a criminal investigation into the death.
Also on Monday, Russia’s consumer protection agency said it had suspended imports from six Ukrainian dairy producers after finding their products violated regulations.
Last week Kiev temporarily suspended seven Russian food companies from selling products in Ukraine.
Ukraine is facing a tough economic situation after Russia’s Gazpromalmost doubled the price of gas it supplies to Ukraine.
The country’s foreign exchange reserves have fallen to about $15bn (£9bn) from $20.42bn on 1 January, Ukraine’s central bank said on Monday. The currency, the hryvnia, has also lost about 30% of its value so far this year.
Eastern Ukraine was the political heartland of Viktor Yanukovych, the pro-Russian president who fled to Russia in February after months of protests.
Russia has branded the new leadership in Kiev illegitimate.