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The threat of military conflict over Crimea has loomed ever larger this week, after troops in Russian army uniforms appeared there. Russia's President Vladimir Putin has claimed that they are local militia who have bought Russian uniforms.

"No one will recognize this referendum, apart from maybe North Korea, Syria and Venezuela," Yatsenyuk said. "I want to be very clearCrimea was, is, and will be an integral part of Ukraine. No concessions. Full stop."

(Read more: Vitali Klitschko: Putin worried over Ukraine)

The U.S. and Russia seemed to be at loggerheads on Friday, after Putin reiterated his wish to protect the Russian-speaking people of Ukraine, and U.S. President Barack Obama announced asset freezes and visa bans on some Russians and Ukrainians accused of threatening Ukraine's sovereignty.

Yatsenyuk, speaking in Kiev, struck a more optimistic note when asked about the possibility of opening negotiations with Russia.

He described the situation as "not as bad as we expected and not good as we need to do."

(Read more: Putin rebuffs Obama as Ukraine crisis escalates)

Yatsenyuk defended his "entirely legitimate" government against Russian claims that it is "fascist." He came to power in February following protests in Kiev against Kremlin-backed Viktor Yanokovych's rule.

He pointed out that the government was supported by the majority of members of Ukraine's parliament, and by minorities who are not usually part of Ukraine's government.

By CNBC's Catherine Boyle. Follow her on Twitter @cboylecnbc.

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Ukraine's PM: No concessions on Crimea

March 6, 2014: Ukraine Prime Minister Arseniy Yatsenyuk at a the NATO aliance headquarters in Brussels.REUTERS

Ukraine Prime Minister Arseniy Yatsenyuk is coming to Washington this week to discuss Russian troops taking control of the Crimea region of his country, the White House confirmed Sunday to Fox News.

President Obama will welcome Yatsenyuk of Ukraine to the White House on Wednesday, according to the administration.

Russian troops began taking control of facilities in the region about a week ago, amid the political uprising in Ukraine in which residents have ousted President Viktor Yanukovych.

Obama has spoken by phone twice with Russian President Vladimir Putin, saying that taking control of Crimea violates Ukraine's sovereignty.

The visit will highlight the United States' support for the people of Ukraine. And the discussions will focus on finding a peaceful resolution to Russias ongoing military intervention and how the international community can help Ukraine confront the resulting economic challenges, the White House said.

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UKRAINE CRISISPM Yatsenyuk to travel toDC this week for talks

Ukraine's first medalist of the Sochi Paralympics dedicated her achievement Saturday to Ukrainian independence and appealed for peace with Russia.

Olena Iurkovska won bronze on the first morning of competition, just hours after Ukraine's Paralympics team decided to attend the 10-day event despite Russia's military occupation of the nearby Crimean peninsula.

Iurkovska finished third in the women's 6 kilometer sitting competition. Svetlana Konovalova of Russia took silver.

"I devote my first medal in Sochi to an independent Ukraine," Iurkovska said. "Every time I race, it will be for Ukrainian independence and peace in my country."

Iurkovska embraced Valentina Matvienko, the speaker of Russia's upper house of parliament, at the post-event flower ceremony.

Later Saturday, Ukraine won two more bronze medals in the biathlon, while Maksym Yarovyi claimed silver in the men's 7.5-kilometer sitting event and Vitaliy Lukyanenko took gold in the visually impaired class.

The crisis in Ukraine has overshadowed the second phase of Putin's bid to use the Winter Games to polish his country's image abroad. Russia's military intervention in Crimea, some 300 miles (475 kilometers) west of Sochi on the Black Sea coast, began after the closing ceremonies of the Olympics two weeks ago.

Rob Harris can be followed at http://www.twitter.com/RobHarris

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Ukraine's 1st Medalist at Sochi Appeals for Peace