(CNN) -- Tensions smoldered in Ukraine, and in capitals around the world on Monday, as Russian troops consolidated their hold on the Ukrainian peninsula of Crimea, global stocks slipped on fears things could get worse and diplomats grasped for a way to stop the situation from escalating.
At an emergency U.N. Security Council meeting to discuss the unfolding crisis, diplomats asked Russia to withdraw its troops and called for mediation.
Russia's envoy said his country's aim in Ukraine is to stop radical extremists who are destabilizing the country -- adding that ousted Ukrainian President Viktor Yanukovych had asked Russia to send troops.
The United States' ambassador accused Russia of breaking international law and responding to an "imaginary threat."
Russian Ambassador Vitaly Churkin read a letter from Yanukovych at the meeting, describing Ukraine as a country "on the brink of civil war," plagued by "chaos and anarchy."
"I would call on the President of Russia, Mr. Putin, asking him to use the armed forces of the Russian Federation to establish legitimacy, peace, law and order, stability, and defending the people of Ukraine," the letter said.
U.S. Ambassador Samantha Power said Russia's claims about the situation in Ukraine were untrue.
"Russian military action is not a human rights protection mission," Power said. "It is a violation of international law."
Ukraine's envoy asked the United Nations for help.
Russian military forces are "illegally occupying Crimea and brutally violating international law and other agreements," Ukrainian Ambassador Yuriy Sergeyev said.
Earlier Monday, British Foreign Secretary William Hague called the situation Europe's most serious crisis of the still-young 21st century.
U.S. President Barack Obama said the United States is examining a series of economic and diplomatic steps to "isolate Russia," and he called on Congress to work with his administration on an economic assistance package for Ukraine.
In Crimea, more Russian troops arrived, surrounding military posts and other facilities and taking effective control of the peninsula from Ukrainian authorities. What they planned to do next remained unclear.
Up to 12 trucks full of Russian troops crossed into the eastern Crimean city of Kerch from Russia Monday, Ukrainian Defense Ministry spokesman Vladislav Seleznyov told CNN.
Additionally, Ukrainian Border Service Assistant Chief Col. Sergei Astakhov said he saw Russian troops move by ferry from Russia across the Strait of Kerch.
As the ferries approached the port, 10 heavily armed troops from the Russian Black Sea Fleet attacked the border post from land and used force to overwhelm Ukrainian border guards, Astakhov said.
In another ominous incident, a Ukrainian Defense Ministry spokesman said the commander of Russia's Black Sea fleet boarded a blocked Ukrainian warship and issued a threat.
"Swear allegiance to the new Crimean authorities, or surrender, or face an attack," he said, according to the spokesman, Seleznyov said.
And one Crimean official has reportedly described the situation in Crimea as quiet.
"Despite hysteria in Ukraine's central media, the situation on the peninsula remains absolutely calm. No conflicts have flared up in Crimea over the past 24 hours. Crimea has preserved its inter-ethnic peace," Crimean First Vice-Premier Rustam Temirgaliyev said, according to Russian state news agency ITAR Tass.
"Not a single armed conflict has been registered in Crimea," Temirgaliyev said. "The 'Crimean spring' is kind and absolutely peaceful."
Despite the assurances, stocks fell around the world, with Russian stocks leading the way as investors parsed the day's developments. Markets declined in Asia, Europe and the United States, where the benchmark Dow Jones was down more than 200 points in mid-afternoon trading.
Although Russia's foreign minister rejected claims his country was acting aggressively, his European Union counterparts met in Brussels to condemn what they called Russia's "clear violation of Ukrainian sovereignty and territorial integrity." They demanded Moscow pull its troops back or face possible sanctions.
Vice President Joe Biden, speaking by telephone to Russian Prime Minister Dmitry Medvedev, warned of increasing political and economic isolation.
State Department spokeswoman Jen Psaki said Monday that sanctions against Russia weren't just possible, but likely.
A senior U.S. administration official told CNN that Russian forces "have complete operational control of the Crimean Peninsula." The official said the U.S. estimates there are 6,000 Russian ground and naval forces in the region.
"There is no question that they are in an occupation position -- flying in reinforcements and settling in," another senior administration official said.
In Kiev, interim Prime Minister Arseniy Yatsenyuk, who has accused Moscow of declaring war, vowed that his West-leaning government would not give up the region.
"Nobody will give Crimea away. ... There are no grounds for the use of force against civilians and Ukrainians, and for the entry of the Russian military contingent," he said. "Russia never had any grounds and never will."
Ukraine's shaky new government has mobilized troops and called up military reservists.
Former Ukrainian Prime Minister Yulia Tymoshenko, released from jail last week, asked the international community for help.
"I am asking all the world, personally every world leader, to use all the possibilities in order to avoid Ukraine losing Crimea," she told CNN's Christiane Amanpour in an interview.
Camouflaged and unidentified
Ukrainian border guards on Monday reported a buildup of armored vehicles on the Russian side of a narrow sea channel dividing Russia and Crimea, Reuters reported, citing a border guard spokesman.
He said that Russian ships had been moving in and around the city of Sevastopol, where the Russian Black Sea Fleet has a base, and Russian forces had blocked mobile telephone service in some areas. The buildup of Russian armor was near a ferry port on the Russian side of the Kerch Channel, opposite the Ukrainian city of Kerch.
Meanwhile, the Ukrainian State Border Security Service said there had been several attacks on border posts in eastern Crimea just along the border with Russia.
Also on Sunday night, unidentified armed men tried to enter the arms depot in Belbek military base near Sevastopol, said Seleznyov, the Ukrainian Defense Ministry spokesman. Ukrainian forces shot into the air to warn them off, but the unidentified men used sound grenades and a Ukrainian commander was wounded as a result, Seleznyov told CNN.
The attackers gained access to the base, but Ukrainian troops retain control of the weapons depot and administration building, Seleznyov added.
Men dressed in both civilian and camouflage gear with red armbands have patrolled the streets of the regional capital, Simferopol. The area has seen several pro-Russia demonstrations with crowds waving Russian flags and shouting "Thank you, Putin."
Navy defector seeks allies
Ten Ukrainian military and naval bases in Crimea were blocked Monday by armed men, the newly appointed naval commander of Ukraine, Rear Admiral Serhei Gayduk, told a Ukrainian TV station.
His predecessor, Denis Berezovsky, who on Sunday said he would not submit to orders from Kiev and defected, was said to have entered the Ukrainian naval base in Crimea under the protection of a group of Cossacks and tried to persuade other Ukrainian officers to defect. However, Gayduk was at the base and urged officers to maintain their allegiance to Ukraine, the Defense Ministry's Seleznyov told CNN. Troops responded by singing the Ukrainian national anthem.
These scenes come after Russian President Vladimir Putin secured permission from his parliament Saturday to use military force to protect Russian citizens in Ukraine and told Obama he had the right to defend Russian interests and nationals, spurning Western pleas not to intervene.
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