Ukraine's interim president Oleksandr Turchnynov later issued a statement placing responsiblity for "the blood of Ukrainian soldiers (on) the leadership of the Russian Federation and specifically President Putin."
Regional defence ministry spokesman Vladislav Seleznyov told AFP the soldier had died after being shot in the neck when a group of gunmen stormed a Ukrainian military base in the northeast of Crimea's main city of Simferopol.
Seleznyov said another soldier was wounded but did not specify whether the base was stormed by Russian soldiers or pro-Kremlin militia who also patrol the peninsula.
But the Ukrainian defence ministry said in a statement the military base was attacked by people "dressed in the military uniforms of servicemen of the armed forces of the Russian Federation."
"For their self defence and protection of their lives, Ukrainian servicemen... deployed in the Autonomous Republic of Crimea are allowed to use arms," the defence ministry said.
Ukrainian authorities had previously forbidden its Crimean soldiers from opening fire - in some cases forcing them to stand guard at their bases with empty rifles - in order not to proke a Russian offensive that could spill into an all-out war.
The defence ministry statement identified the first Ukrainian victim as warrant officer S. V. Kakurin.
There was no immediate reaction to the reported death from either Russian authorities in Moscow or the peninsula's rebel leadership.
Simferopol base seized
Defence ministry spokesman Seleznyov said pro-Russian forces had by late Tuesday taken complete control of Ukraine's Simferopol base.
"The centre has been taken under their full control. All the servicemen inside were lined up in a row and their documents seized," he said.
"They were all informed that they were under arrest."
Seleznyov said he could not immediately say how many Ukrainian soldiers had been arrested or the number of pro-Russians involved in the attack.
Russian forces took de facto control of the peninsula at the beginning of March after the toppling last month of the pro-Kremlin regime in Ukraine and the rise to power of a new Western-backed administration that is seeking closer ties with the European Union.
Ukraine's navy chief Sergiy Gayduk had told the same government meeting that an officer had been shot and injured in the leg "during an attack against a base in Simferopol."
He did not specify where or when the attack happened or who was behind it, and it was not immediately clear if it was the same incident.
An AFP reporter outside a Ukrainian military unit in a suburb northeast of Simferopol heard a burst of gunfire coming from the building and saw two ambulances driving into the area.
The region around the military unit was sealed off by what appeared to be pro-Moscow militants.
"Armed attempts to take over (Ukrainian) military units have multiplied in recent days," Gayduk said.
US warns Russia to expect more sanctions
The White House vowed early this morning to level more sanctions against Russia for its moves to take over the Crimea.
"We condemn Russia's moves to formally annex'' Crimea, White House spokesman Jay Carney said, noting that there had already been sanctions designations against Russian officials.
"There are more to come,'' he warned.
Carney said Obama spoke by telephone with German Chancellor Angela Merkel on the next steps to take on Crimea and how to support Ukraine.
G7 crisis meeting called for next week
Earlier, Obama called for a G7 summit next week in the Hague to discuss the escalating showdown over Russia's annexation of Crime.
"The United States and the other members of the G7 have already suspended our preparations for the G8 Summit in Sochi,'' said National Security Council spokeswoman Caitlin Hayden.
"Today President Obama invited his counterparts from Canada, France, Germany, Italy, Japan, the United Kingdom, and the EU to a meeting of G7 leaders next week on the margins of the Nuclear Security Summit in The Hague.
"The meeting will focus on the situation in Ukraine and further steps that the G7 may take to respond to developments and to support Ukraine.''
Russian forces had seized the peninsula Crimea at the beginning of March after the toppling last month of the pro-Kremlin regime in Ukraine and the rise to power of a new Western-backed administration that is seeking closer ties with the European Union.
Call that punishment? Moscow scoffs at sanctions
Meanwhile Russia has brushed off the toughest sanctions issued by the United States and European Union against Moscow since the end of the Cold War, by acknowledging the sovereignty of Crimea.
Washington began to take aim at Vladimir Putin's inner circle yesterday, in response to Sunday's vote in Crimea in favour of secession from Ukraine. Two of President Putin's top aides were among 11 officials hit first by an assets freeze and travel ban.
But Putin appeared unmoved by the measures, signing a decree only hours later recognising Crimea's sovereignty. He was expected to use a scheduled appearance before the Russian Parliament to recommend moving forward with incorporating Crimea into the Russian Federation.
However, Russia has appeared immune to any diplomatic retribution.
Scepticism the sanctions would inflict little financial pain on Russia, particularly if those targeted have no assets in the US or have already moved them beyond America's reach, was quickly fuelled by Russian reaction to the move.
Rogozin tweeted: "Comrade Obama ... what will you do with those who have neither accounts nor property abroad? Or didn't you think of that?"
- Independent, AP