Russia and the rest of the OSCE have agreed to deploy civilian monitors to Ukraine, but there is no mention if they will go to Crimea.
The OSCE, which works by consensus, says up to 500 monitors will gather information on the security situation in Ukraine and any violations of the rights of minorities. The mission will last six months.
The United States says the OSCE has a mandate to work in all of Ukraine, including Crimea. But Russia's ambassador to the OSCE, Andrey Kelin, said Crimea is part of Russia and the mission has no mandate there.
Russia has thwarted several efforts to deploy monitors in Crimea. Pro-Russian forces stopped OSCE military observers from crossing into Crimea last week.
In the Kremlin Friday, Russian President Vladimir Putin signed a law completing the annexation of Crimea. The law recognizes parliament's approval of this week's referendum by Crimeans on breaking away from Ukraine.
The U.S. says no one in the international community will recognize Crimea as part of Russia.
In Brussels, Ukraine's interim Prime Minister Arseniy Yatsenyuk signed a political association agreement with the European Union.
The EU also added 12 more Russian and Crimean officials to a list of people subject to travel bans and asset freezes. There are now 33 people on the list, including Russian Deputy Prime Minister Dmitry Rogozin and Dmitry Kiselyov -- the head of Russia's state-run Rossiya Segodnya news agency.
The United States also has imposed sanctions on Russian officials -- including several members of President Putin's inner circle. President Barack Obama says he is considering more penalties against entire sectors of the Russian economy.
The Russian Foreign Ministry said Friday that Russia will "respond harshly" to new sanctions. Moscow already has imposed travel bans on nine Americans, including Republican Senator John McCain, Democratic Senate Majority Leader Harry Reid and Republican Speaker of the House of Representatives John Boehner.
Also Friday, U.S. Defense Secretary Chuck Hagel spoke for nearly an hour with Russian Defense Minister Sergei Shoigu. A Pentagon spokesman says Shoigu assured Hagel that troops carrying out war games along Ukraine's southeastern border have no plans to enter Ukraine.