Ukrainian lawmakers were set to consider a presidential request for the introduction of martial law in the country on Monday following an incident in which Russian coast guard ships fired on Ukrainian navy vessels.
An emergency meeting of the United Nations Security Council was also called for Monday. The European Union and NATO called for restraint from both sides.
Ukrainian President Petro Poroshenko said at a meeting of Ukraine's national security council Monday that "we demand that (the ships and crews) are urgently turned over to the Ukrainian side" and called for a "de-escalation" of the crisis around Crimea.
The Ukrainian navy said six of its seamen were wounded when Russian coast guards opened fire on three Ukrainian ships near the Kerch Strait and then seized them late Sunday.
Russia's Federal Security Service that is in charge of the coast guard said that three Ukrainian sailors were lightly injured and given medical assistance. It said the Ukrainian boats were towed to the nearby port of Kerch.
The two nations traded blame over the incident that further escalated tensions that have soared since Russia annexed Ukraine's Crimean Peninsula in 2014 and backed a separatist insurgency in eastern Ukraine.
Ukraine said its vessels were heading to the Sea of Azov in line with international maritime rules, while Russia charged that they had failed to obtain permission to pass through the Kerch Strait separating Crimea from the Russian mainland.
The narrow strait is the only passage between the Black Sea and the Sea of Azov. It's spanned by a 19-kilometer (11.8-mile) bridge that Russia completed this year.
Dozens of far-right protesters burned tires outside the Russian consulate Monday in the western Ukrainian city of Lviv. The protest was organized by the National Corps party, which also called for a demonstration in front of Poroshenko's office in the capital, Kiev. The group, which is small but can put pressure on Ukraine's leadership, argues Poroshenko isn't aggressive enough against Russia.
Poroshenko chaired an emergency meeting of his Cabinet early Monday and asked parliament to introduce martial law in response to what he described as Russian aggression.
"We consider it as an act of aggression against our state and a very serious threat," the president said. "Unfortunately, there are no 'red lines' for the Russian Federation."
Russia, meanwhile, says Ukraine started it.
"Three Ukrainian ships which were involved in a provocation in Russian territorial waters have been delivered to the port of Kerch. The crews were obviously acting intentionally," Russian Foreign Ministry spokeswoman Maria Zakharova told reporters. "As we understand it, this provocation and the complex of provocative actions have been planned ahead of time."
Russia closed the Kerch Strait for sea traffic Sunday by positioning a tanker under the bridge spanning it. It reopened the route early Monday.
The seizure of the Ukrainian ships followed a tense situation in which the three Ukrainian vessels were maneuvering near the Kerch Strait for hours shadowed by Russian coast guard boats.
The incident came after months of tensions and incidents in the Sea of Azov that involved inspections and seizures of ships.
While a 2003 treaty designates the Kerch Strait and Sea of Azov as shared territorial waters, Russia has sought to assert greater control over the passage since the annexation of Crimea.