After an hour-long telephone call, Putin said in a statement that Moscow and Washington were still far apart on the situation in the former Soviet republic, where he said the new authorities had taken "absolutely illegitimate decisions on the eastern, southeastern and Crimea regions.
Read: Diplomacy will resolve Ukraine crisis: Obama to Putin
"Russia cannot ignore calls for help and it acts accordingly, in full compliance with international law," Putin said.
The most serious east-west confrontation since the end of the Cold War escalated on Thursday when Crimea's parliament, dominated by ethnic Russians, voted to join Russia. The region's government set a referendum for March 16 - in just nine days' time.
European Union leaders and Obama denounced the proposed referendum as illegitimate, saying it would violate Ukraine's constitution.
Read: Ukraine crisis: Crimea votes to join Russia
Read: Putin discusses Crimea proposal to join Russia
Before calling Putin, Obama announced the first sanctions against Russia since the start of the crisis, ordering visa bans and asset freezes against so far unidentified persons deemed responsible for threatening Ukraine's sovereignty.
Japan endorsed the Western position that Russia's actions constitute "a threat to international peace and security" on the crisis after Obama spoke to Prime Minister Shinzo Abe.
The EU, Russia's biggest economic partner and energy customer, adopted a three-stage plan to try to force a negotiated solution but stopped short of immediate sanctions.
Brussels and Washington also rushed to strengthen the new authorities in economically shattered Ukraine, announcing both political and financial assistance.
In their telephone call, Obama said he urged Putin to accept the terms of a potential diplomatic solution, and said the dispute over Crimea could be resolved in a way that took account of Russia's legitimate interests in the region.
Putin was defiant on Ukraine, where he said pro-Russian President Viktor Yanukovich had been overthrown in an "anti-constitutional coup" last month. But he stressed what he called "the paramount important of Russian-American relations to ensure stability and security in the world", the Kremlin said.
"These relations should not be sacrificed for individual differences, albeit very important ones, over international problems," Putin said.
He maintained Moscow was not behind the seizure of Crimea, home of Russia's Black Sea Fleet. Russia says the troops without national insignia that have surround Ukrainian bases are "local self-defence units". The West has ridiculed this argument.
Watch: Shiv Shankar Menon on Ukraine crisis
After talks in Rome on Thursday, US secretary of state John Kerry said Russian foreign minister Sergei Lavrov was personally delivering proposals to Putin to end the crisis.
Kerry said the executive order signed by Obama on Thursday provided a legal framework for imposing sanctions but also left open the door for dialogue.
The 28-nation EU welcomed Ukrainian Prime Minister Arseny Yatseniuk to its emergency summit, even though Kiev is neither a member nor a recognised candidate to join the bloc, and agreed to bring forward the signing of the political parts of an agreement on closer ties before Ukraine's May 25 elections.
Read: Russia Today's news anchor quits on air over Ukraine
"No one will give up Crimea to anyone," Yatseniuk told a news conference in Brussels, while Ukraine's acting president, Oleksander Turchinov, called the planned referendum "a farce, a fake, a crime".
The European Commission said Ukraine could receive up to 11 billion euros in the next couple of years provided it reaches agreement with the International Monetary Fund, which requires painful economic reforms like ending gas subsidies.
Despite Putin's tough words, demonstrators who have remained encamped in Kiev's central Independence Square to defend the revolution that ousted Yanukovich said they did not believe Crimea would be allowed to secede.
Some said they were willing to go to war with Russia, despite the mismatch between the two countries' armed forces.
"We are optimists. Crimea will stand with us and we will fight for it," said Taras Yurkiv, 35, from the eastern city of Lviv. "How we will fight depends on the decisions of our leadership. If necessary, we will go with force. If you want peace, you must prepare for war."
Alexander Zaporozhets, 40, from central Ukraine's Kirovograd region, put his faith in international pressure.
"I don't think the Russians will be allowed to take Crimea from us: you can't behave like that to an independent state. We have the support of the whole world. But I think we are losing time. While the Russians are preparing, we are just talking."
On the ground in Crimea, the situation was calm although 35 unarmed military observers dispatched by the pan-European Organisation for Security and Cooperation in Europe were denied entry into the peninsula after landing in the southern Ukrainian port of Odessa.
A UN special envoy who travelled to the regional capital Simferopol on Tuesday was surrounded by pro-Russian protesters, some of them armed, and forced to leave on Tuesday. The United Nations said it was sending its assistant secretary-general for human rights to the region soon.
In eastern Ukraine, police on Thursday ejected pro-Russian demonstrators who had occupied government headquarters in the city of Donetsk, Yanukovich's home town, ending a siege that Kiev saw as part of a Russian plan to create a pretext to invade.