Russia did not immediately or directly respond to the allegation, but Russian news agencies cited the FSB security service as saying it had incontrovertible proof that Ukraine had orchestrated what it called "a provocation" and would make its evidence public soon.
Ukrainian President Petro Poroshenko immediately called a meeting with his top military and security chiefs to discuss the situation, which involved two small Ukrainian armoured artillery vessels and a tug boat.
Russia annexed Crimea in 2014 and then built a giant road bridge linking it to southern Russia which straddles the Kerch Strait - a narrow stretch of water which links the Black Sea to the Sea of Azov which is home to two of Ukraine's most important ports.
Russia's control of Crimea, where its Black Sea Fleet is based, and of the bridge, mean it is able to control shipping flows.
A Reuters witness said Russia backed its blockade with at least two Sukhoi Su-25 warplanes which screeched overhead, while Russian state TV said Russian combat helicopters had been deployed in the area.
The Ukrainian navy said on social media that six Ukrainian sailors had been wounded in the subsequent seizure of its ships which appear to have been rammed and boarded and that the alleged Russian attack on them had occurred after they had retreated and headed back towards Odessa, the Black Sea port from where they had begun their journey.
"After leaving the 12-mile zone, the Russian Federation's FSB (security service) opened fire at the flotilla belonging to ... the armed forces of Ukraine," it said in a statement.
The European Union in a statement said it expected Russia to restore freedom of passage via the Kerch strait and urged both sides to act with utmost restraint to de-escalate the situation. A NATO spokeswoman issued a similar appeal to both sides.
RISK OF WIDER CONFLICT
With relations still raw after Russia's annexation of Crimea and its backing for a pro-Moscow insurgency in eastern Ukraine, the incident risks pushing the two countries towards a wider conflict.
A bilateral treaty gives both Russia and Ukraine the right to use the Sea of Azov, which lies between them and is linked by the narrow Kerch Strait to the Black Sea. Since Russia annexed Crimea, tension has risen with both countries complaining about shipping delays and harassment.
Earlier on Sunday, Russia's border guard service had accused Ukraine of not informing it in advance of the three ships' journey, something Kiev denied.
Russia said the Ukrainian ships had been manoeuvring dangerously and ignoring its instructions with the aim of stirring up tensions.
Russian politicians denounced Kiev, saying the incident looked like a calculated bid by Poroshenko to increase his popularity ahead of an election next year.
In another sign of rising tensions, Russia's state-controlled RIA news agency reported on Sunday night that Ukrainian forces had started heavy shelling of residential areas in eastern Ukraine which is controlled by pro-Moscow separatists.
Reuters could not independently confirm that and the Interfax news agency cited separatists as denying there had been any unusual escalation.
The latest crisis initially erupted after Russia tried and failed to intercept the three Ukrainian ships in the Black Sea, accusing them of illegally entering Russian territorial waters.
The Ukrainian navy said a Russian border guard vessel had rammed the tug boat and damaged it in that early incident.
It said its vessels had every right to be where they were and that the ships had been en route from the Black Sea port of Odessa to Mariupol, a journey that requires them to go through the Kerch Strait. (Writing by Andrew Osborn Editing by Richard Balmforth)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)