Arseniy Yatsenyuk called for a halt to military movements in Crimea, but said his country is refusing to respond with force.
Defence Minister Igor Tenyukh on Saturday told a cabinet meeting that Russia began sending reinforcements on Friday "without warning or Ukraine's permission."
Tenyukh said 6,000 Russian troops have been sent to the peninsula, in violation of the law. He added Russia has about 80 military vehicles stationed in various areas of Crimea.
Russia is supposed to notify Ukraine of any troop movements outside the Black Sea Fleet naval base it maintains in Sevastopol under a lease agreement with Ukraine.
Russian forces on Saturday attempted to penetrate a marine battalion in the Crimean city of Feodosiya, Tenyukh said.
The apparent troop mobilization is the latest escalation following the ouster of Ukraine's pro-Russian president last week by a protest movement aimed at turning Ukraine toward the European Union and away from Russian influence.
CBC News correspondent Susan Ormiston is in Sevastopol, on the southern edge of Crimea, not far from where Russia has its naval base.
Russia has had the Black Sea naval base for many decades and wants to hold on to it.
"We're now seeing Russian troops in other parts of Crimea, armoured personnel carriers, as well as attack helicopters, and we're hearing Russia may be trying to take an anti-aircraft missile base this morning," Ormiston said.
In another development, the newly installed leader of Ukraine's Crimea region declared himself in charge of local military and law enforcement on Saturday.
Sergei Aksyonov said the armed forces, the police, the national security service and border guards in the region will answer only to his orders.
Ukraine's population is divided in loyalties between Russia and Europe, with much of western Ukraine advocating closer ties with the European Union while eastern and southern regions look to Russia for support. Crimea is mainly Russian-speaking.
British Foreign Secretary William Hague says he has been in contact with Russian Foreign Minister Sergei Lavrov. Hague says he called for a de-escalation of military involvement in Crimea and respect for Ukrainian sovereignty.
On Friday, the White House told the U.K.'s Guardian newspaper that said U.S. officials are consulting with European leaders on the possibility of pulling out of the G8 summit in Russia this June.
Back in Moscow, the speaker of the upper house of parliament, Valentina Matviyenko, said Saturday that Russia could deploy additional troops to Crimea to help protect the local population from the new Ukrainian authorities.