Ukraine's Interior Minister Arsen Avakov has tweeted a video showing what appears to be a large ship ramming into the side one of the nation's vessels.
Ukrainian authorities said the footage was taken in the Kerch Strait from on board a Russian ship, the larger of the two ships.
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They said it showed "openly aggressive action" by the Russian border patrol ship.
The Ukrainian military claims Russian boats opened fire and seized three ships during the incident, but Russian authorities denied this.
They claim three Ukrainian warships entered Russian waters illegally, justifying the seizures.
Mr Avakov said the video will be "proof in the international court", and warned Russia to "look forward to the reactions of friendly countries".
The incident increases tensions between the volatile countries in a stand-off over the Kerch Strait.