Ukraine will not "hand over Crimea to anyone," Ukrainian Prime Minister Arseniy Yatsenyuk said Monday.
Moscow deployed its forces in Ukraine's Crimean Peninsula, a majority Russian-speaking region, claiming it was protecting ethnic Russians and Russia's interests in the area.
The pro-Russian groups that have seized buildings in Crimea will be prosecuted, Yatsenyuk said in a press conference in Kiev.
Ships from Russia's Baltic and Northern fleets have joined the forces from the Black Sea Fleet in the Crimean port city of Sevastopol, Ukrainian officials said.
Sevastopol has been the home of Russia's Black Sea Fleet since the 18th century.
Russian Prime Minister Dmitry Medvedev, meanwhile, announced plans in Moscow to build a bridge linking Russia to the Crimean Peninsula, which Soviet leader Nikita Khrushchev gave to Ukraine in 1954.
Russia and Ukraine's ousted government had signed an agreement calling for construction of the bridge.
"We have made decisions that are binding, particularly documents that were signed in December of last year that have not been modified or disavowed by anyone," Medvedev said, referring to the bridge over the Kerch Strait.
Diplomats scrambled on Monday to find a peaceful resolution to the standoff between Ukraine and Russia over Crimea.
U.N. Secretary-General Ban Ki moon called on Moscow and Kiev to avoid taking actions that will raise tensions further, while the European Union foreign ministers urged the two countries to engage in a dialogue.
Spanish Foreign Minister Jose Manuel Garcia-Margallo, who traveled to Brussels for the emergency meeting of the bloc's foreign ministers, called for respect for the sovereignty of Ukraine and compliance with international law, which requires "the withdrawal of Russian forces" from Crimea.
The Crimean Peninsula, located on the northern coast of the Black Sea, is home to 2 million people; ethnic Russians make up 60 percent of the population, while 25 percent of residents are ethnic Ukrainians and 12 percent are Crimean Tatars.
U.S. President Barack Obama warned Russia about a military intervention in Crimea last Friday.
"We are now deeply concerned by reports of military movements taken by the Russian Federation inside Ukraine," Obama said, warning that there would be "costs" if a military intervention occurred.
The developments in Crimea pose an immediate challenge for Ukraine's new authorities, who were installed after the ouster of President Viktor Yanukovych, a Kremlin ally, following deadly protests last week.
The crisis that led to Yanukovych's ouster erupted at the end of November, when Yanukovych backed away from plans to ink a pact with the European Union and instead signed a $15 billion financial-aid package with Russia.
Protesters took to the streets of Kiev and began occupying administrative buildings, prompting Ukraine's parliament, then controlled by Yanukovych's allies, to pass a package of laws on Jan. 16 restricting freedom of assembly, freedom of speech and other basic rights.
Violent clashes pitting demonstrators and riot police broke out three days later and left six dead and hundreds wounded.
Ukrainian officials and opposition leaders began seeking a negotiated solution to the crisis in the wake of the bloodshed.
The talks led to the resignation of Prime Minister Mykola Azarov on Jan. 28 and the repeal of the controversial anti-protest laws.
But more street battles pitting pro-European Union protesters against the security forces left dozens dead in February, and led to Yanukovych agreeing to call early presidential elections and then fleeing Kiev.
After Yanukovych left the city, many of his former allies in parliament turned against him and helped oust him from power and release his arch-rival, the Fatherland's Yulia Tymoshenko, from prison.
She has reportedly announced her candidacy in the presidential election, which has been moved up to May 25.
Yanukovych, meanwhile, surfaced last week in Russia, which has received a request from Ukraine for his extradition on mass murder charges. EFE