Ukrainian defence sources have accused Russia’s military of demanding the surrender of their forces in Crimea.
Russia’s Black Sea Fleet chief Aleksander Vitko threatened a full assault if they did not surrender by dawn on Tuesday, the sources said.
However, Interfax news agency later quoted a Russian spokesman denying that any ultimatum had been issued.
The EU and US are threatening to hit Moscow with sanctions and travel bans over its intervention in Crimea.
Meanwhile, Russia’s UN envoy has said ousted Ukrainian President Viktor Yanukovych has asked Russia to use military force in Ukraine.
Vitaly Churkin said in a speech at the UN that Mr Yanukovych had made the request in writing to Russian President Vladimir Putin.
Countries have frequently attempted to justify interventions on the basis that a government has requested help to put down a rebellion.
No shots have been fired and no treaties signed but Crimea is now de facto under Russian armed control.
Two large Ukrainian military bases are surrounded, with Russian troops standing alongside local self-defence groups, who demand that the Ukrainian soldiers inside defect from Kiev to Crimea’s new pro-Russia government.
The naval headquarters remains blockaded and key installations like airports are still occupied. Thousands of newly arrived Russian elite troops far outnumber Ukraine’s military presence here. Crimea has in effect been cut off by roadblocks, where vehicles are being denied access to the peninsula.
At countless pro-Russia demonstrations, Moscow’s intervention is warmly welcomed. But away from the nationalist fervour, Crimeans from all sides are profoundly fearful of what comes next.
The trouble began last month when Mr Yanukovych was ousted following months of street protests.
Since then, Russia has sent thousands of troops into Crimea, surrounding military bases and taking control of airports.
The Kremlin says its troops are needed to protect civilians in the region, many of whom are Russian speakers and have welcomed Russia’s intervention.
Moscow, which does not recognise the new government, says people in Crimea have come under threat from “ultra-nationalists” since the revolution in Kiev.
Ukraine has ordered full mobilisation to counter the intervention.
No shots have yet been fired in the region, but Russia’s apparent threats have intensified the rhetoric.
Reports said Ukrainian military chiefs at various bases had been told to leave their bases by Tuesday morning.
The commanders of two warships similarly told Ukrainian TV they had been given even tighter deadlines to surrender, but they had vowed instead to fight for Ukraine.
US President Barack Obama has once again accused Russia of violating international law and said Moscow was “on the wrong side of history”.
American officials say they are planning to target Russian individuals and organisations with economic sanctions.
They have also once again urged Moscow to withdraw troops from Crimea, and have proposed sending international monitors to Ukraine.
The EU is also preparing to hit Moscow with sanctions.
It was gathered that the EU may even try to have Russia thrown out of the forthcoming football World Cup.
Ukraine’s Prime Minister Arseniy Yatsenyuk said earlier that any attempt to seize Crimea would fail, urging allies to give economic and political support to his government.