The unprecedented incident occurred in the Kerch Strait, a narrow waterway that gives access to the Sea of Azov that is used by Ukraine and Russia.
The Ukrainian navy said in a statement posted on Facebook on Sunday evening that one of its small artillery boats, the Berdyansk, was damaged and one crew member was injured.
A later statement said Russian special forces had seized three Ukrainian vessels in the Black Sea and two other sailors had been injured.
Russia's Federal Security Service (FSB) issued a statement late Sunday saying it used weapons to force Ukrainian ships to stop after they ignored legitimate demands and maneuvered dangerously. It said it impounded three vessels after they illegally crossed the Russian border, and opened a criminal case into the violation.
The statement added that the three wounded Ukrainian crew members were not in critical condition and were receiving medical treatment.
Ukrainian President Petro Poroshenko convened an emergency meeting of his military cabinet late Sunday to address the incident, according to a tweet by Presidential Spokesman Svyatoslav Tsegolko.
Moscow responded to Kiev's allegations by stating it has evidence that Ukraine is responsible for the clashes.
The FSB said in an earlier statement Sunday night that "there is irrefutable evidence that Kiev prepared and orchestrated provocations ... in the Black Sea. These materials will soon be made public."
Russian Foreign Ministry spokeswoman Maria Zakharova said on Facebook that the incident was characteristic of Ukrainian behavior: provoke, pressure and blame for aggression.
The Kerch Strait, which Russia blocked earlier Sunday, is the only passage into the Sea of Azov beyond it. The strait is crossed by the recently completed Kerch Bridge, connecting Crimea to Russia. Transit under the bridge has been blocked by a tanker ship, and dozens of cargo ships awaiting passage are stuck.
The incident began earlier Sunday after the Ukrainian navy claimed a Russian coast guard vessel rammed a Ukrainian navy tugboat, which was traveling with two Ukrainian navy artillery boats from Odessa on the Black Sea to Mariupol in the Sea of Azov, via the Kerch Strait.
"Russian coast guard vessels ... carried out openly aggressive actions against Ukrainian navy ships" during the transit, the Ukrainian navy statement said. It said a Russian coast guard ship damaged the tugboat's engine, hull, side railing and a lifeboat.
The statement added that Russia had been informed in advance about the planned transit.
Russia's Federal Security Service, known as the FSB, told Russian news agencies Sunday that the Ukrainian ships held their course and violated Russian territorial waters, which were temporarily closed. The FSB accused the Ukrainian navy of staging a provocation against Russia.
"Their goal is clear," an FSB statement said — "to create a conflict situation in the region." The statement didn't mention ramming a Ukrainian tugboat.
Though a 2003 treaty designates the Kerch Strait and Sea of Azov as shared territorial waters, Russia has been asserting greater control over the passage since 2015.
The Ukrainian Foreign Ministry said in a statement that Russia's actions were a violation of the U.N. Charter and international law, and pledged to "promptly inform our partners about Russia's aggressive actions."
"Such actions pose a threat to the security of all states in the Black Sea region," the statement said, "and therefore require a clear response from the international community."
Dmitry Kiselyov, a commentator on the state-controlled Rossiya channel, told viewers of his Sunday evening news program that Ukrainian President Petro Poroshenko — encouraged by the U.S. — is looking to pick a fight with Russia in the Black Sea.
The talk show host also said that the U.S. talked Poroshenko into staging a provocation against Russia as a means to disrupt the upcoming meeting between Presidents Vladimir Putin and Donald Trump at this week's Group of 20 summit in Argentina.
"What is happening now at the (Kerch) bridge threatens to turn into a very unpleasant story," Kiselyov warned.