Russian forces took control of the Black Sea peninsula in late February following the toppling of Moscow-backed Ukrainian President Viktor Yanukovich by protests provoked by his decision to spurn a trade deal with the European Union last November and seek closer ties with Russia. People in Crimea voted overwhelmingly in the weekend referendum to join Russia.
Ukrainian and Russian troops have avoided violent confrontations, with Kiev anxious to avoid giving Moscow a reason for overrunning its bases in Crimea.
However, Ukraine's pro-Western prime minister Arseny Yatseniuk denounced Tuesday's death of the serviceman as a "war crime" and called for international talks to prevent an escalation of the conflict.
A defence ministry statement said the dead man had been shot while manning a tower, adding that the attackers in Russian uniforms were holding the base commander in a nearby building. A Russian Defence Ministry spokesman declined immediate comment.
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Interfax Ukraine news agency, quoting Crimean police, said a member of the pro-Russian "self-defence forces" was also killed in the incident. The report could not immediately be confirmed.
In Kiev, the press service of Acting President Oleksander Turchinov announced new military orders. "In connection with the death of a Ukrainian serviceman ... Ukrainian troops in Crimea have been allowed to use weapons to defend and protect the lives of Ukrainian servicemen," the order issued by the defence ministry said.
Turchinov also accused Russia of annexing Crimea in actions reminiscent of Nazi Germany's takeover of Austria and Czechoslovakia's Sudetenland in the run-up to World War Two.
Putin's speech drew immediate hostile reaction in Kiev and the West.
U.S. Vice President Joe Biden called Moscow's action a "land grab" and on a visit to Poland stressed Washington's commitment to defending the security of NATO allies on Russian borders.
Polish Prime Minister Donald Tusk said Russia's move was unacceptable to the international community, while Britain suspended military cooperation with Russia.
"It is completely unacceptable for Russia to use force to change borders, on the basis of a sham referendum held at the barrel of a Russian gun," British Prime Minister David Cameron said, threatening Putin with "more serious consequences".
(Watch: Putin: No intention on splitting Ukraine)
In his speech, the Russian leader lambasted Western nations for what he called hypocrisy, saying they had endorsed Kosovo's right to self-determination and independence from Serbia but now denied Crimeans the same rights.
"You cannot call the same thing black today and white tomorrow," Putin declared, saying that while he did not seek conflict with the West, Western partners had "crossed the line" over Ukraine and behaved "irresponsibly".
Ukraine's new leaders, in power since the overthrow of Yanukovich, included "neo-Nazis, Russophobes and anti-Semites", he added.
Putin tried to reassure Ukrainians that Moscow did not seek any further division of their country. Fears have been expressed in Kiev that Russia might move on the Russian-speaking eastern parts of Ukraine, where there has been tension between some Russian speakers and the new authorities.
"Don't believe those who try to frighten you with Russia and who scream that other regions will follow after Crimea," Putin said. "We do not want a partition of Ukraine."
Putin said Russian forces in Crimea had taken great care to avoid any bloodshed, contrasting it with NATO's 1999 campaign to drive Serbian forces out of Kosovo. Reinforcements had remained within the treaty limit of 25,000 troops in the area, he said.
Setting out Moscow's view of the events that led to the overthrow of Yanukovich last month, Putin said the "so-called authorities" in Kiev had stolen power in a coup, opening the way for extremists who would stop at nothing.
Making clear Russia's concern at the possibility of the U.S.-led NATO military alliance expanding into Ukraine, he declared: "I do not want to be welcomed in Sevastopol (Crimean home of Russia's Black Sea fleet) by NATO sailors."
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Moscow's seizure of Crimea has caused the most serious East-West crisis since the end of the Cold War, and Putin showed no sign of backing down despite the threat of tougher sanctions.
In Crimea, where his speech and the signing ceremony were broadcast live, his words were greeted with rapture by some.
"Putin's done what our hearts were longing for," said Natalia, a pensioner who sells snacks in a kiosk in the centre of Simferopol. "This finally brings things back to what they should be after all those years. For me, for my family, there can be no bigger joy, for us this is sacred."
Yatseniuk earlier tried to reassure Moscow on two of its main concerns, saying in a televised address delivered in Russian that Kiev was not seeking to join NATO and would disarm Ukrainian nationalist militias.
On Monday, the United States and the EU imposed sanctions on a handful of officials from Russia and Ukraine accused of involvement in Moscow's seizure of the Black Sea peninsula, the majority of whose 2 million residents are ethnic Russians.
Russian politicians responded to the sanctions with defiance. The State Duma, or lower house, adopted a statement urging Washington and Brussels to extend the visa ban and asset freeze to all its members.
Foreign Minister Sergei Lavrov threatened retaliation. "The sanctions introduced by the United States and the European Union are unacceptable and will not remain without consequences," the foreign ministry said in a statement about a telephone call Lavrov made to U.S. Secretary of State John Kerry.
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The White House said leaders of the world's leading industrial democracies would hold a Group of Seven meeting without Russia on the sidelines of a nuclear security summit in The Hague next week to consider further responses to the crisis.
Despite strongly worded condemnations, Western nations have been cautious in their first practical steps against Moscow, both to leave the door open for a diplomatic solution and out of reluctance to endanger the world economic recovery.
Russian stocks gained another 2 percent after rallying strongly on Monday, and the rouble rose after Putin said Russia would not seek to further divide Ukraine. Investors noted the initial sanctions did not target businesses or executives.
But Russia said its long-delayed privatisation program could be postponed again.
Washington and Brussels have said future punitive measures could affect the economy, energy and arms contracts as well as the private wealth of magnates close to Putin.