Sunday's incident has sparked worldwide condemnation over Russia's use of force.
Ukrainian troops have been fighting Russian-backed separatists in eastern Ukraine since 2014, a conflict that has left over 10,000 dead, but fighting has eased since a truce in 2015.
The FSB said it had been forced to act because the ships - two small Ukrainian armored artillery vessels and a tug boat - had illegally entered its territorial waters, attempted illegal actions, and ignored warnings to stop while maneuvering dangerously.
The European Union will next month consider further sanctions against Russian Federation over the latest flare-up in the Ukraine conflict, the foreign minister of Austria, which holds the rotating EU presidency, said on Tuesday.
"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.
Antonio Guterres said he was "greatly concerned" about the situation and called on "both parties to exercise maximum restraint and to take steps without delay to contain this incident and reduce tensions".
"The officers of the Ukrainian special service were carrying out assignments regarding counter-intelligence support for a Ukrainian naval formation, as provided for under paragraph 12 of Ukraine's law on the security service", Hrytsak was quoted as saying in an SBU press statement issued early on November 27.
Poroshenko delivered a speech to Ukraine's parliament asking it to approve the declaration of martial law starting Wednesday, with the military already on full alert. Russian officials accuse Poroshenko of trying to manufacture a crisis to boost his desperately low poll ratings ahead of next year's presidential elections, which he appears to be in danger of losing.
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"I have to emphasize that, according to the global law, Crimea and respective territorial waters are the Ukrainian territory temporarily occupied by the Russian Federation", Ukraine's UN Ambassador Volodymyr Yelchenko told the Security Council.
Ukraine declared martial law in part of the country following what it called Russia's "act of aggression".
U.S. secretary of state Mike Pompeo later issued a statement saying that the USA "condemns this aggressive Russian action".
The tugboat was escorting two Ukrainian naval vessels from Odessa on the Black Sea to the port city of Mariupol on the Sea of Azov via the Kerch Strait when the incident occurred.
The European Union, Britain, France, Poland, Denmark, and Canada all condemned what they called Russian aggression.
In a phone conversation with German Chancellor Angela Merkel, Mr Putin expressed "serious concern" over the introduction of martial law, the Kremlin said in a statement. Last month, Ukraine announced it would build a new military base on the Azov Sea to counter the Russian presence.
Meanwhile, US President Donald Trump told reporters outside the White House Tuesday that he was "not happy about it at all", but refused to take the belligerent stance his United Nations envoy, Nikki Haley, adopted the previous day. "We're all working on it together", Mr Trump told reporters at the White House. North Atlantic Treaty Organisation has called for calm, and an emergency United Nations Security Council meeting will be convened Monday to discuss the issue.