"The steps taken by the legitimate leadership of Crimea are based on the norms of international law and aim to ensure the legal interests of the population of the peninsula," said Putin, according to the Kremlin.
Following an extraordinary Sunday meeting of the Ukrainian government, Prime Minister Arseniy Yatsenyuk announced that he will meet with Obama in Washington on Wednesday on a "resolution of the situation in Ukraine," the Interfax news agency reported. The White House confirmed the meeting.
"Our country and our people are facing the biggest challenges in the history of modern independent Ukraine," the prime minister said earlier in the day. "Will we be able to deal with these challenges? There should only be one answer to this question and that is: yes."
In an emotional climate of crisis, Ukraine on Sunday solemnly commemorated the 200th anniversary of the birth of its greatest poet, Taras Shevchenko, a son of peasant serfs who is a national hero and is considered the father of modern Ukrainian literature.
"This is our land," Yatsenyuk told a crowd gathered at the Kiev statue to Shevchenko. "Our fathers and grandfathers have spilled their blood for this land. And we won't budge a single centimeter from Ukrainian land. Let Russia and its president know this."
"We're one country, one family and we're here together with our kobzar (bard) Taras," said acting President Oleksandr Turchynov.
Later, Ukrainians in the tens of thousands massed in the Kiev's center for a multi-faith prayer meeting to display unity and honor Shevchenko. One of the speakers, former imprisoned Russian tycoon Mikhail Khodorkovsky, almost burst into tears as he implored the crowd to believe not all Russians support their country's recent actions in Ukraine.
"I want you to know there is a completely different Russia," Khodorkovsky said.
In the eastern city of Luhansk, however, people who gathered in a square to celebrate Shevchenko's birthday were attacked by pro-Russia protesters, and some were beaten up, local media reports said.
Chanting "Russia! Russia!" the demonstrators then broke through a police barricade and took over the local government building, where they raised the Russian flag and demanded a citywide referendum on joining Russia, Channel 5 and other local media reported.
But it's Crimea, a strategic peninsula in the Black Sea, that has become the chief flashpoint in the battle for Ukraine, where three months of protests sparked by President Victor Yanukovych's decision to ditch a significant treaty with the 28-nation European Union after strong pressure from Russia led to his downfall.
A majority of people in Crimea identify with Russia, and Moscow's Black Sea Fleet is based in Sevastopol, as is Ukraine's.
In Simferopol, Crimea's capital, a crowd of more than 4,000 people turned out Sunday to endorse unification with Russia. On Lenin Square, a naval band played World War II songs as old women sang along, and dozens of tricolor Russian flags fluttered in the cold wind.
"Russians are our brothers," Crimean Parliament speaker Vladimir Konstantinov said. He asked the crowd how it would vote in the referendum a week hence.
"Russia! Russia!" came the loud answer.