Said Sen. John McCain, R-Ariz.: "I guess this means my spring break in Siberia is off."
Obama also signed a new executive order that would allow him to sanction key Russian industries, actions that could have a harsher impact on that country's economy. Senior administration officials said Russia's energy, financial services and metals and mining sectors are among the industries that could be targeted.
"Russia must know that further escalation will only isolate it further from the international community," Obama said.
The U.S. has so far acted in conjunction with the European Union, Russia's largest trading partner. The EU's close economic ties with Russia gives its penalties more bite, but also leave the alliance more vulnerable if the Kremlin retaliates.
The EU did not immediately release the names of those it had targeted Thursday with travel bans and asset freezes. European leaders, meeting in Brussels, also announced plans to scrap an EU-Russia summit scheduled for June. And like Obama, they warned that further provocations by Russia would result in deeper punishments.
"We need to prepare to take further steps and we need to do it together," said Swedish Prime Minister Fredrik Reinfeldt. "A strong Europe is the last thing that Putin wants. He wants to split us up."
German Chancellor Angela Merkel said that beyond increasing the number of people affected by asset freezes and travel bans — initially 21 politicians and military commanders — the leaders would prepare for possible measures at a higher level, which would include economic sanctions and an arms embargo.
Russia's economy has already taken a hit during the Crimea crisis. The country's stock market fell 10 percent this month, potentially wiping out billions. Economists have slashed growth forecasts to zero this year, and foreign investors have been pulling money out of Russian banks.
The West's dispute with Russia is expected to dominate Obama's trip to Europe next week. He'll chair a hastily arranged meeting of the Group of Seven, pointedly leaving out Russia, which often joins the U.S., Britain, France, Germany, Italy, Canada and Japan to comprise the Group of Eight.
Officials said the G-7 leaders will discuss what kind of financial assistance they can provide to the fledgling Ukrainian government. The G-7 nations have also suspended preparations for a G-8 summit that Russia is scheduled to host this summer in Sochi, site of the recently completed Winter Olympics.
Associated Press writers Lynn Berry in Moscow and Robert Burns in Washington contributed to this report.
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