Video of the incident released by Ukrainian officials appeared to show a Russian ship ramming the Ukrainian tugboat.
"Russian coastguard vessels ... carried out openly aggressive actions against Ukrainian navy ships", Ukrainian authorities said in a statement, revealing that the tugboat's engine, hull, railings, and lifeboat were damaged in the incident.
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.
"We call on Russian Federation to respect its worldwide obligations and not obstruct or harass Ukraine's transit in the Kerch Strait, to release the seized Ukrainian ships and crew and to de-escalate the tensions it has created", Haley told the Council, CBS News' Pamela Falk reported.
During an emergency UN Security Council meeting to defuse rising tensions after the confrontation, US Ambassador Nikki Haley called the incident "yet another reckless Russian escalation" and demanded that the Kremlin release the sailors.
But the Ukrainian Foreign Ministry stated that Russia's actions were a violation of the UN Charter and global law.
Andriy Drach said on camera he was on the Nikopol gunboat with an order to sail from Odessa to Mariupol.
Seized Ukrainian seamen speak on Russian TV, and it is not clear if they are speaking under duress. "At the same time, we have to work for de-escalation". "As stated in our Crimea Declaration, the United States rejects Russia's attempted annexation of Crimea".
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US President Donald Trump suggested it was up to European governments to handle the crisis. "And hopefully it will get straightened out", Trump told reporters as he left the White House.
On November 25, Russia's Federal Security Service (FSB) border guards fired on and seized three Ukrainian naval vessels in the Kerch Strait area.
"I condemn Russian use of force in Azov Sea". "What are they claiming, that Ukrainian sailors committed a crime by crossing the Russian border?"
Russia's ongoing militarization of Crimea, the Black Sea and the Sea of Azov, poses further threats to Ukraine's independence.
The crisis unfolded as two small Ukrainian warships and a tugboat were heading through the Kerch Strait, a waterway that gives access to the Sea of Azov from the Black Sea and which is used by both Ukraine and Russian Federation. The FSB said only three had suffered non-life threatening injuries and were given medical treatment.
"And this will continue, forevermore", the service said, adding that the presence of its agents on board Ukrainian naval vessels was not "astonishing".
Russian Foreign Minister Sergey Lavrov accused Ukraine of violating global norms with "dangerous methods that created threats and risks for the normal movement of ships in the area".
Squabbles over control of the Azov Sea and the Kerch Strait, which connects to the Black Sea to the south, are nothing new. A newly built Russian bridge opened by Putin himself now spans the strait, which Moscow hopes will solidify its claim to adjoining Crimea, the Ukrainian peninsula it forcibly annexed in 2014.
He said, "the number of units that have been deployed along our border -- what's more, along its full length -- has grown dramatically".