The groups demand that the government declare martial law.
As world leaders denounced Russia's aggression against Ukraine, President Donald Trump waited more than a day before offering a muted response about the clash, leaving the task of criticizing Moscow to the outgoing USA ambassador to the UN.
The approved measures included a partial mobilisation and strengthening the country's air defences.
Russia's security agency also filmed three men, identified as an SBU counterintelligence agent, a Navy officer and a sailor.
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It unilaterally annexed the peninsula after a referendum in March 2014, but failed to garner worldwide support and recognition for the move while prompting the USA and the E.U.to impose sanctions.
The sea incident has raised fears of a wider military escalation.
"What we saw yesterday was very serious", Stoltenberg told a news conference after an emergency meeting of the Western military alliance held on request on Ukraine. Ukraine accuses Russian Federation of militarizing the Azov Sea and harassing Ukrainian ships. Ukraine said it had notified Russian authorities in advance of the three ships' movements - in line with the 2003 accord - and denied they had done anything wrong.
The United States and the European Union have slapped sanctions on Russian businesses, tycoons and banks for Russia's annexation of Crimea.
German Foreign Minister Heiko Maas said any Russian "blockade" of the Sea of Azov was "unacceptable" and proposed French-German mediation to resolve the crisis.
The Kerch Strait is the only passage into the Sea of Azov beyond it.
The incident took place on Sunday as three Ukrainian naval ships were transiting from Odessa on the Black Sea to Mariupol in the Sea of Azov, via the Kerch Strait.
The sailors, including the commander of a small Ukrainian gunboat, will be held under formal arrest in a detention center in Simferopol until January 25, the judge ruled. The FSB said only three had suffered non-life threatening injuries and were given medical treatment.
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"I condemn Russian use of force in Azov Sea". More than 10,000 people have died in the fighting.
"The crisis in the Sea of Azov has been building for a long time and has not received enough worldwide attention", he told DW in an email.
"It doesn't matter if we are talking about the detention of Russian ships or ships of foreign states", he said.
Their way through the strait was blocked by a Russian tanker placed under the new bridge connecting Russia with Crimea, which was completed earlier this year.
He said, "the number of units that have been deployed along our border -- what's more, along its full length -- has grown dramatically". But Ukraine says the incidents happened in areas that are free to shipping.
The opening of an additional front at sea, even if Ukraine lacks a real navy, introduced an unstable element into what had been a shadowy war.
An extraordinary meeting of NATO-Ukraine ambassadors is planned in Brussels later Monday.
Some Ukrainian opposition politicians have speculated that he is using the introduction of martial law as an excuse to postpone the elections. "This raises concerns that.it could lead to postponement of the presidential election", it said.
Russian Federation 'fires on and seizes' Ukrainian naval ships
Moscow had prevented the ships from entering the Kerch Strait by placing a large cargo vessel beneath a Russian-controlled bridge. The incident flared up over the weekend in an escalation of tensions over the Russian-annexed Crimean peninsula.