By Richard Balmforth and Natalia Zinets

KIEV (Reuters) - Protests in eastern Ukraine in which pro-Russian activists seized public buildings in three cities are part of a plan to destabilize Ukraine and bring in Russian troops, Prime Minister Arseny Yatseniuk said on Monday.

Saying Russian troops were within a 30 km (19 mile) zone from the Ukrainian border, Yatseniuk told a government meeting: "An anti-Ukrainian plan is being put into operation ... under which foreign troops will cross the border and seize the territory of the country.

"We will not allow this," he said.

Pro-Russian protesters in the east seized official buildings in three cities - Kharkiv, Luhansk and Donetsk - on Sunday night, demanding that referendums be held on whether to join Russia.

A similar move preceded a Russia-backed takeover of Crimea in March followed by annexation of the peninsula by Russia.

Interior Minister Arsen Avakov said on Monday the main regional administration building in Kharkiv had been cleared of "separatists".

But police said protesters occupying the state security building in Luhansk had seized weapons and highway police had closed off roads into the city.

"Unknown people who are in the building have broken into the building's arsenal and have seized weapons," a police statement said. Nine people had been hurt in the disturbances in Luhansk.

Mainly Russian-speaking eastern Ukraine has seen a sharp rise in tension since Moscow-backed Ukrainian President Viktor Yanukovich's overthrow in February and the advent of an interim government in Kiev that wants closer ties with Europe.

Russia has branded the new leadership in Kiev illegitimate and has annexed Ukraine's Crimea region, citing threats to its Russian-speaking majority - a move that caused the biggest standoff between Moscow and the West since the end of the Cold War.

YANUKOVICH CALL

The protesters appeared to be responding in part to Yanukovich, who fled to Russia after he was ousted and who on March 28 issued a public call for each of Ukraine's regions to hold a referendum on its status inside the country.

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Separately, Ukraine's defense ministry said a Russian marine had shot and killed a Ukrainian naval officer in Crimea on Sunday night.

The 33-year-old officer, who was preparing to leave Crimea, was shot twice in officers' quarters in the locality of Novofedorovka. It was not clear why the Russian marine had opened fire.

Yatseniuk said that though much of the unrest had died down in eastern Ukraine in the past month there remained about 1,500 "radicals" in each region who spoke with "clear Russian accents" and whose activity was being coordinated through foreign intelligence services.

But he said Ukrainian authorities had drawn up a plan to handle the crisis.

"We have a clear action plan," he said, adding that senior officials would head to the towns concerned.

Avakov on Sunday accused Russian President Vladimir Putin of orchestrating the "separatist disorder" and promised that disturbances would be brought under control without violence.

Russia has been pushing internationally a plan proposing the "federalization" of Ukraine in which regions of the country of 46 million would have broad powers of autonomy.

Ukraine, while drawing up its own blueprint of constitutional changes for 'de-centralization' in which smaller municipalities would be able to develop their own areas by retaining a portion of state taxes raised, says the Russian plan is aimed at breaking up the country.

Referring to the Russian plan, Yatseniuk said: "It is an attempt to destroy Ukrainian statehood, a script which has been written in the Russian Federation, the aim of which is to divide and destroy Ukraine and turn part of Ukraine into a slave territory under the dictatorship of Russia," he said.

"This is not going to happen," he said.

"I appeal to the people and the elites of the east. Our common responsibility is to preserve the country and I am sure that no-one wants to be under a neighboring country. We have our country. Let's keep it," he said.

(Additional reporting by Thomas Grove and Pavel Polityuk, and Lina Kushch in Donetsk; Editing by Angus MacSwan)