Several dozen ships were anchored near the strait as they waited for the standoff to be solved, marine traffic tracker website VesselFinder.com showed on Sunday.
Russian military ships were also deployed near the bridge.
Early on November 25, Kyiv said a Russian coast guard vessel rammed a Ukrainian Navy tugboat in the same area as three Ukrainian ships that sailed out of the Black Sea port of Odesa approached the Kerch Strait in an attempt to reach the Sea of Azov port at Mariupol.
The latest incident comes after the Ukrainian navy in September complained of "acts of provocation" by Russian border guards against its ships taking the same route. Moscow alleged that Ukrainian ships had been manoeuvring dangerously and ignoring its instructions with the aim of stirring up tensions.
"Russia's provocative actions in the Black Sea and the Sea of Azov have crossed the line and become aggressive", it said.
"Russian ships have violated our freedom of maritime navigation and unlawfully used force against Ukrainian naval ships". The strait is crossed by the recently completed Kerch Bridge, connecting Crimea to Russian Federation.
Later, pro-Russian separatists took over parts of Donbass in southeastern Ukraine. In particular, Don border guard cruiser rammed the Ukrainian armored artillery boat, which led to the damage of the main engine, planting and accommodation rail, life float is lost.
Russian Federation said the Ukrainian ships had illegally entered its waters in a deliberate act of provocation.
Ukraine's foreign ministry said in a statement it wanted a clear response to the incident from the global community.
The FSB statement did not mention the ramming of the Ukrainian tugboat.
Russia's FSB, which runs the country's border guards, said the Ukrainian vessels "illegally entered a temporarily closed area of Russian territorial waters" and accused Kiev of failing to notify Russia about the ships' movements in advance.
"Such things are not carried out without the head of state's knowledge, consent, and - I think - initiative", Pushkov told Russia's state-run Rossia 24 TV channel.