Ukrainian President Petro Poroshenko has instructed all military units near Crimea and in the easterly Donbass region to be at the highest level of combat readiness, following allegations of a Ukrainian incursion into Crimea.
Separately, the spokesman for Ukraine's General Staff said Ukraine had been holding scheduled military exercises in southern Ukraine since yesterday.
Russian President Vladimir Putin accused Kiev of using terrorist tactics to try to provoke a new conflict and destabilise Crimea, which Moscow annexed from Ukraine in 2014.
Ukraine dismissed the allegations as a cynical pretext for Russia to make more military threats against Ukraine.
Meanwhile, Ukraine's UN envoy said a build-up of Russian military on Ukraine's border with the Crimean region could reflect "very bad intentions".
The warning came after the UN Security Council discussed the growing tensions.
Ukrainian UN Ambassador Volodymyr Yelchenko, who requested the closed-door meeting of the 15-member council, said Russia had amassed more than 40,000 troops in Crimea, seized by Moscow in 2014, and on the Ukrainian border.
"These numbers may reflect some very bad intentions and this is the last thing we would like to happen," he told reporters.
"My biggest hope is that this discussion (in the council) will help the Russian Federation to understand that they cannot really continue with this kind of behaviour," Mr Yelchenko said.
Russian UN Ambassador Vitaly Churkin dismissed concerns about a Russian military build-up. He described the Security Council meeting as "useful" to explain the situation.
"Instead of counting our military they should be bringing an end to the conflict in Donetsk and stop shelling civilians in Donetsk and Luhansk," Mr Churkin told reporters after the meeting.
Pro-Russian separatists are fighting the Kiev government's forces in the eastern Ukraine region despite a fragile ceasefire.
Civilian casualties from shelling, mines and booby traps in eastern Ukraine are at their highest in a year, the United Nations' human rights chief has said.
A peace plan for the eastern Donbass region of Ukraine, negotiated in Minsk between Ukraine and Russia by Germany and France some 18-month ago, has stalled for months.
The Security Council has discussed Ukraine dozens of times since Russia annexed Crimea in 2014, but has been deadlocked on the topic as Moscow is one of the body's five veto powers.
More than 9,500 people have been killed since the pro-Russian insurgency erupted in April 2014.
