U.S. Ambassador Samantha Power said many supporters recognize that "if such a blatant violation of a nation's borders is left unchecked, the consequences for other nations could be severe."
She said it was also important to note that only a handful of states supported Russia and many, like Russia, "fear free expression and peaceful assembly."
"Today's vote shows that despite significant misinformation spread by Russia, the truth of what Russia has done in Crimea has penetrated to all the regions of the world," Power said.
The resolution adopted Thursday says the referendum on Crimea has "no validity" and calls on all countries and organizations not to recognize Russia's annexation.
It also calls on all parties to immediately pursue a peaceful resolution of the situation in Ukraine "through direct political dialogue" and to refrain from "inflammatory rhetoric that may increase tensions."
Deshchytsia, the Ukrainian foreign minister, told AP his country plans to go back to the Security Council, despite Russia's veto, and will take its case against the annexation of Crimea to other international organizations and individual countries. He said that will include holding an "intensive dialogue" at the Ukraine-NATO ministerial meeting next week.
When asked about the possibility of a formal link between NATO and Ukraine, which Russia strongly opposes, Deshchytsia said "we are talking about all possible options to resolve this conflict."
He said the government's position remains to solve the situation peacefully and diplomatically and NATO membership "at the moment is not on agenda." It would require a decision of parliament for Ukraine to apply for membership in the Western military alliance, he said.
Ukraine needs "good relations ... partnership relations with Russia, and good contact between people of Ukraine and people of Russia," Deshchytsia said.
But in response to the latest situation, Ukraine signed an association agreement with the European Union last Friday "and this direction is supported by the Ukrainian people and gives us an additional argument to say that Ukraine is part of Europe," he said.
Associated Press writer Cara Anna contributed to this report from the United Nations.
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