Reading from a text, an unidentified, bearded man said protesters would call on Russia to send in a peacekeeping force in the event of aggressive action by what he described as the "illegitimate" authorities in Kiev.
The group's leaders later went on to the square in front of the building and read the same text by loud-hailer to a crowd of about 1,000, some of whom shouted: "Hurrah! Hurrah!".
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Pro-Russia activists moved into public buildings in two other cities - Kharkiv and Luhansk - in the mainly Russian-speaking east of Ukraine on Sunday evening with similar demands for referendums to be held on their status.
Saying Russian troops were within a 30-km (19-mile) zone on the other side of the Ukrainian border, Prime Minister Arseny Yatseniuk told an emergency government meeting on Monday that the action was part of a Russian-written script for seizing control of parts of Ukraine following the takeover of Crimea.
"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.
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Separately, a Russian soldier shot dead a Ukrainian naval officer in eastern Crimea, Ukraine's Defence Ministry said on Monday, the second Ukrainian death reported since Russia took control of the Black Sea peninsula.
Russian President Vladimir Putin has praised the military's largely bloodless takeover of Crimea after it voted in a referendum last month to join Russia but the death may boost the already high tension between Russia and Ukraine.
"The Russian marine killed the unarmed officer. He killed the major with two shots," said Ukrainian navy spokesman Vladislav Seleznyov.
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Kiev has blamed Russia for stoking tensions in mostly Russian-speaking eastern Ukraine, where pro-Russian protesters have seized state security offices in Donetsk and Luhansk, including facilities where weapons are stored.
The defense ministry spokesman said the soldier had been preparing his belongings to leave for the Ukrainian region of Mykolaev on Wednesday when an argument broke out with Russian servicemen.
The officer, Stanislav Karachevsky, who was married and had two children, was killed with an AK-74 on the fifth floor of the dormitory where he lived, he said.
A defense ministry statement said another Ukrainian soldier had been beaten by Russian servicemen and detained, but gave few details.
The first reported death occurred in Simferopol when an unknown gunman shot and killed a Ukrainian serviceman while he was manning a tower overlooking a vehicle pool at the base.
A defense ministry statement said the attackers had been wearing Russian military uniforms and were holding the base commander in a nearby building.
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