The neighbours have been locked in a tense tug-of-war since Russia's 2014 annexation of Crimea, but the incident in which Russian coast guard ships fired on Ukrainian navy vessels directly pitted the two militaries, placing them on the verge of an open conflict.
Ukrainian politicians were set to consider a presidential request for the introduction of martial law in the country later on Monday.
The Ukrainian navy said six of its seamen were wounded when Russian coast guards opened fire late on Sunday on three Ukrainian ships near the Kerch Strait and then seized them.
Russia said three Ukrainian sailors were lightly injured and given medical assistance.
Ukraine's president, Petro Poroshenko, chaired an emergency meeting of his cabinet early on 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."
Martial law could entail a variety of measures including closing the borders, imposing restrictions on foreigners entering the country, a ban on gun sales, a ban of any political gatherings and rallies and even closing down media outlets if they are deemed a threat to national security.
An emergency meeting of the United Nations Security Council was also called for Monday, while the European Union and NATO called for restraint from both sides.
Mr Poroshenko had a phone call with NATO secretary-general Jens Stoltenberg to discuss the situation, and NATO later said that, at Mr Poroshenko's request, its ambassadors and Ukraine's envoy will hold emergency talks in Brussels later.
NATO said Mr Stoltenberg expressed the US-led military alliance's "full support for Ukraine's territorial integrity and sovereignty, including its full navigational rights in its territorial waters under international law".
European Union chief Donald Tusk called on Russia to stop provoking Ukraine and urged the authorities to return any Ukrainian ships or sailors it is holding.
The European Council president tweeted: "I condemn Russian use of force in Azov Sea", and added that "Russian authorities must return Ukrainian sailors, vessels and refrain from further provocations".
He said he has discussed developments with Mr Poroshenko and will meet the Ukrainian leader's representatives later.