Russia's FSB security service, which oversees border forces, confirmed weapons had been fired and the vessels seized
Russian President Vladimir Putin warned Ukraine against any "reckless acts" on Tuesday after Kiev declared martial law in response to Moscow's seizure of three of its navy vessels.
The Ukrainian parliament late on Monday voted in favour of President Petro Poroshenko's request for the introduction of martial law in parts of the country for 30 days.
The decision came as Ukraine and Russia face their most dangerous crisis in years after Russian forces fired on, boarded and captured Kiev's ships on Sunday off the coast of Crimea.
The incident was the first major confrontation at sea in the long-running conflict pitting Ukraine against Moscow and Russian-backed separatists in the country's east.
It has raised fears of a wider escalation in a conflict that has killed more than 10,000 people since 2014 and prompted international calls for restraint and offers of mediation.
Martial law gives Ukrainian authorities the power to mobilise citizens with military experience, regulate the media and restrict public rallies in affected areas.
Moscow has accused Kiev of planning Sunday's confrontation as a provocation aimed at drumming up support for Poroshenko ahead of elections next year and convincing Western governments to impose further sanctions on Russia.
In a phone conversation with German Chancellor Angela Merkel, Putin expressed "serious concern" over the introduction of martial law, the Kremlin said in a statement.
Putin said Kiev's actions were "clearly taken in view of the election campaign in Ukraine".
He said he hoped Berlin could intervene with Ukrainian authorities "to dissuade them from further reckless acts".
Sunday's incident has been playing out on Russian and Ukrainian television screens, with dramatic footage of Russian ships chasing down a Ukrainian tugboat that was trying to pass through the Kerch Strait from the Black Sea into the Sea of Azov.
Ukraine has accused Russian border patrol vessels of ramming the tugboat, which was accompanied by two small warships, and of firing on the Ukrainian vessels.
Russia's FSB security service, which oversees border forces, confirmed weapons had been fired and the vessels seized, but accused Ukrainian ships of crossing illegally into Russian waters and of ignoring warnings.
Tensions have been building for months over the Kerch Strait, especially after Russia built a new bridge across the waterway that gives it a land connection to Crimea, annexed by Moscow in 2014.
Moscow has so far resisted calls to release the three ships or the 24 sailors it has detained, suggesting they could face criminal action.
In a move sure to further anger Kiev, Russian state television late on Monday aired footage of some of the captured sailors being questioned by Moscow's security services.
One of the sailors is heard saying "the actions of the Ukrainian armed vessels in the Kerch Strait had a provocatory character" parroting the version of events put forward by Russian authorities.
Western governments have rallied behind Kiev in the dispute, accusing Russia of illegally blocking access to the Sea of Azov and of taking military action without justification.
Kiev urged the United States and European Union to impose more sanctions on Russia over the latest incident.
Britain, Canada, France, Germany and others expressed support for Kiev on Monday, with EU President Donald Tusk calling for Russia to return the Ukrainian sailors and ships and "refrain from further provocations".
The United Nations Security Council met in an emergency session on the crisis on Monday, where US envoy Nikki Haley called the seizure of the ships an "outrageous violation of sovereign Ukrainian territory" and slammed "yet another reckless Russian escalation".
She did not, however, threaten further sanctions on Russia and President Donald Trump suggested it was up to European governments to handle the crisis.
"We don't like what's happening and hopefully it will get straightened out. I know Europe is not they are not thrilled. They're working on it too. We're all working on it together," Trump told reporters at the White House.