The two artillery boats and a tugboat "unlawfully entered a temporarily closed area of Russia's territorial sea at about 7 am Moscow time this morning," Russia's Border Control Service told the Interfax news agency. "It is clear that their goal is to create a conflict situation in the region."
Ukraine disputes this. The Ukrainian Foreign Ministry said in a statement that Russia acted "aggressively" and "illegally used force against the ships of the Ukrainian Navy." A Russian ship rammed into the tugboat, damaging it, the Ukrainian navy added.
A bilateral treaty grants both countries the right to use the Azov Sea.
The standoff raises the spectre of further confrontation between Russia and Ukraine.
Ukraine called for an emergency meeting of the UN Security Council. The European Union called on Russia to reopen the Kerch Strait and urged "all to act with utmost restraint to de-escalate the situation immediately."
A lot is at stake. The two countries have been at loggerheads since a pro-Moscow government in Ukraine was toppled more than four years ago, touching off Russia's annexation of Ukraine's Crimea Peninsula and the ongoing war in eastern Ukraine involving pro-Russian separatists.
Fighting between the rebels and Ukrainian troops has claimed more than 10,300 lives since 2014, and continued skirmishes result in near-daily casualties.
Ukraine has pledged to respond to the incident. "We will react in a dynamic manner," said Ukrainian Navy spokesman Oleh Chalyk. "In contrast to the Russian Federation, we act according to international law."
According to the Ukrainian Navy, Russia sent two combat helicopters to the location of the incident. Local media reported that dozens of ships, both cargo and those with tourists, are stuck on the Black Sea.
The Ukrainian ships were on a journey through the Black Sea, having left the Ukrainian port city of Odessa and heading to Mariupol on the Azov Sea coast, the government-controlled Ukrainian city that is closest to the breakaway regions of Donetsk and Luhansk.
Since President Vladimir Putin earlier this year opened the new bridge across the Kerch Strait - connecting the Russian mainland to Crimea - Moscow has increased its control of the area.
Tensions between Russia and Ukraine have been steadily mounting in recent months, and even entering new battlefields.
Last month, the conflict spilled over into the area of faith when the Ukrainian Orthodox Church officially broke free from Moscow's control, a move that continues to anger the Kremlin.
Amid the Black Sea standoff, popular Russian TV host Dmitry Kiselyov told state television that Ukrainian President Petro Poroshenko was picking a fight with Russia at the prompting of the United States.
"What is happening now at the (Kerch) bridge threatens to become a very unpleasant story," said Kiselyov, one of the Kremlin's main propagandists.
