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 clear—Crimea 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.