The White House says the situation in Ukraine will be "front and center" during President Barack Obama's trip to Europe next week.
National Security Advisor Susan Rice told reporters Friday that the common theme to the president's trip is the fundamental strength of U.S. partnerships and alliances, including NATO, the European Union and the G7.
Rice said Ukraine and the Russian takeover of Crimea are prompting a fundamental reassessment of U.S.-Russian relations. She said the world will clearly see that Russia is more and more isolated.
Deputy National Security Advisor Ben Rhodes said a G-7 summit in The Hague -- a meeting that probably would have included Russia as an eighth member -- has been added to the president's agenda as part of that isolation.
Also on the president's European schedule is a nuclear security summit with more than 50 other countries, including Russia.
Rice said the United States has every interest in continuing to cooperate with Russia on this issue, which she calls a pillar of the Obama national security policy -- making it harder for terrorists to get their hands on nuclear materials.
Meanwhile, Russia and the rest of the OSCE [the Organization for Security and Cooperation in Europe] agreed Friday 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, including human rights.
The United States said 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.
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Russian President Vladimir Putin Friday signed legislation completing the annexation of Crimea, while Ukraine initialed a deal for closer political cooperation with the European Union.
The Kremlin signing ceremony took place after the Federation Council, the upper house of Russia's parliament, voted unanimously to incorporate the Crimea region into Russia. The lower house ratified the treaty on Thursday, just four days after Crimean residents voted in a referendum to break away from Ukraine and join Russia.
President Putin and Crimean leaders signed the treaty on Tuesday, and the Kremlin said the treaty came into force on the date it was signed.
In Brussels, meanwhile, Ukraine's interim Prime Minister Arseniy Yatsenyuk signed a political association agreement with the European Union. Also Friday, the EU added 12 people - all Russian or Crimean - to a list of those subject to travel bans and asset freezes, raising the number of such individuals to 33.
Among those newly added to the EU sanctions list are Russian Deputy Prime Minister Dmitry Rogozin and Dmitry Kiselyov, the controversial TV anchor who heads the Russian government's Rossiya Segodnya news agency.
The United States has also imposed sanctions on Russian officials - including several members of President Putin's inner circle - and a prominent Russian bank.
President Barack Obama says he is considering more penalties against entire sectors of the Russian economy. He says those plans are being formulated in conjunction with European allies.
In a meeting Friday with his advisory Security Council, Putin said for now, Russia will hold off on imposing sanctions on the United States in retaliation for U.S. sanctions against Russia over the Ukraine crisis.
However, his spokesman, Dmitry Peskov, told reporters separately that Russia will respond in kind to the latest U.S. sanctions, which target Russian officials and members of President Putin's inner circle. "We will respond every time," Peskov said.
And the Russian Foreign Ministry said in a statement Friday that Russia will "respond harshly" to the latest round of U.S. sanctions.
On Friday, British Prime Minister David Cameron warned the Kremlin that Russia would face far reaching consequences if it sent troops into Ukraine after a referendum in Crimea which he said has been carried out under the barrel of a Kalashnikov.
"The best rebuke to Russia is a strong and successful Ukraine,'' Cameron said, adding that if Russian troops went into eastern Ukraine then the Kremlin would face "far-reaching consequences in a broad range of economic areas.''
Cameron also said that Russia is more dependent on Europe than Europe is on Russia.