President Barack Obama insists the future of Ukraine must be decided by the people of Ukraine.
In a White House statement on Monday, Obama said Ukraine's territorial integrity must be respected.
Obama's executive order issued Monday names seven Russian government officials. The United States also says it identifies and targets the assets of other individuals who aren't government officials but are supporting them. The sanctions come against officials the White House says have contributed to the crisis in Ukraine.
Sanctions include asset freezes and travel bans on officials from Russia and Ukraine.
The Treasury Department also is imposing sanctions on four Ukrainians, including former President Viktor Yanukovych and two Crimea-based separatist leaders.
The U.S. announcement came shortly after the European Union announced travel bans and asset freezes on 21 people.
Over the weekend, a Kremlin-backed referendum to join Russia was overwhelmingly approved by voters in Ukraine's Crimean region.
The sanctions were highly anticipated after the vote.
Obama says new U.S. sanctions imposed on Russian officials make it clear "that there are consequences for their actions" in Crimea and he's warning that the U.S. stands ready to impose further sanctions if necessary.
Russian President Vladimir Putin is expected to speak on the Crimea situation in a special address to the Russian parliament on Tuesday.