Sunday's incident has sparked global condemnation over Russia's use of force.
Russia and Ukraine have been locked in long-simmering conflict since the annexation of the Black Sea peninsula of Crimea by Russia in 2014, and a war with Russian-backed separatists in the country's east has claimed more than 10,000 lives.
Vasyl Hrytsak, the head of the SBU, confirmed that his officers were on board to support the military and said one of them had been seriously wounded after Russian aircraft fired missiles at the Ukrainian vessels. "We call on Russian Federation to return to Ukraine its vessels and detained crew members, and to respect Ukraine's sovereignty and territorial integrity within its internationally recognized borders, extending to its territorial waters".
Russia has so far refused to release them saying the sailors had crossed illegally into Russian waters and had also ignored warnings from its border guards.
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". Poroshenko promises that martial law would not mean Ukraine's immediate mobilization for war or the restriction of civil rights.
Back in Kiev, Ukrainian President Petro Poroshenko declared Monday that he would seek parliamentary approval to introduce a 60-day state of martial law in Ukraine-a declaration that anxious many domestic and global observers, with some even wondering about the fate of Ukraine's not-so-robust democratic institutions.
Calling Russia's capture of Ukrainian seamen "unacceptable", the European Union's foreign policy chief, Federica Mogherini, urged Russia to "immediately release" them and provide them with medical aid.
"We consider it as an act of aggression against our state and a very serious threat", Mr Poroshenko said.
In response to the Kerch Strait incident, Poroshenko wants to impose martial law in Ukraine for the next 30 days. Russian politicians have accused Poroshenko of deliberately instigating the standoff to boost his flagging popularity ahead of elections in March.
Ukrainian navy accuses Russia of seizing three ships after allegedly firing on them near Crimea
An announcement posted on the Kremlin's official website on the ratification of the treaty with Ukraine governing use of the sea of Azov and Kerch strait.
"The United States will continue to stand with the people of Ukraine against the Russian aggression", she added later.
Several countries have condemned Russia's actions on Monday, and the UN Security Council failed to agree a Russian-proposed agenda, and instead discussed a Ukrainian proposal on the issue.
Sunday's incident has been playing out on Russian and Ukrainian television screens, with dramatic footage of Russian ships chasing down a Ukrainian tugboat that was trying to pass through the Kerch Strait from the Black Sea into the Sea of Azov.
There was a risky escalation on Sunday in the long-running crisis between Ukraine and Russia, as the Russian coast guard attacked and seized three Ukrainian military ships and their crew. The Strait links the Azov Sea to the Black Sea.
Putin and German Chancellor Angela Merkel spoke on the phone early Tuesday, and the Russian president expressed a "serious concern" about what the martial law in Ukraine might entail.
While other US officials took a strong stand behind Ukraine, President Donald Trump seemed more equivocal.
With tensions spilling over, German Foreign Minister Heiko Maas suggested on Tuesday that Germany, France, Russia and Ukraine could work together to resolve the tensions between Moscow and Kiev.
Meanwhile, the Kremlin warned Tuesday the declaration of martial law might trigger a flare-up of hostilities in eastern Ukraine. In a brief statement Monday afternoon, he told reporters: "We do not like what's happening, either way, we don't like what's happening and hopefully it will get straightened out".
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