Speaking in front of a crowd gathered in Kiev to commemorate the 200th anniversary of poet and nationalist Taras Shevchenko, Arseniy Yatsenyuk said: "This is our land. Our fathers and grandfathers have spilled their blood for this land.
"And we won't budge a single centimetre from Ukrainian land. Let Russia and its president know this."
Mr Yatsenyuk later announced he would fly to the US this week for high-level talks on the "resolution of the situation in Ukraine".
Russia has reinforced its armed presence on the Crimean peninsula, with Russian president Vladimir Putin's foreign minister ruling out any dialogue with Ukraine's new authorities, whom he dismissed as the puppets of extremists.
The regional parliament in Crimea is to hold a referendum on March 16 on leaving Ukraine to join Russia.
Senior lawmakers in Moscow have said they would support the move, ignoring sanctions threats and warnings from US president Barack Obama that the vote would violate international law.
Foreign Secretary William Hague said Russia's occupation of Crimea would prove a "big miscalculation", as he sought to keep up pressure for a diplomatic solution.