Russia fired on and then seized three Ukrainian ships on Sunday, accusing them of illegally entering its waters in the Sea of Azov, in a dramatic spike in tensions that raises fears of a wider escalation.

NATO chief Jens Stoltenberg held phone talks with Ukrainian President Petro Poroshenko, and officials from the two sides will meet later in the day.

"The Secretary General expressed NATO's full support for Ukraine's territorial integrity and sovereignty, including its full navigational rights in its territorial waters under international law," NATO said of Stoltenberg's call.

Kiev demanded the return of its ships and sailors, denouncing "another act of armed aggression" by Russia, which annexed Crimea from Ukraine in 2014.

The Ukrainian military has been put on high alert and the country's parliament is to vote on a request by Poroshenko to impose martial law for 60 days.

Ukraine has also urged its Western allies to step up existing sanctions implemented against Russia over Crimea and its role in the ongoing conflict in eastern Ukraine between the government and pro-Moscow separatists.

Moscow blamed Kiev for the incident, with Foreign Minister Sergei Lavrov accusing Ukraine of a planned provocation and of using "dangerous methods" that put ships in the area at risk.

Russian denials drew a barbed response on Twitter from the US Special Envoy for Ukraine Negotiations, Kurt Volker.

"Russia rams Ukrainian vessel peacefully traveling toward a Ukrainian port. Russia seizes ships and crew and then accuses Ukraine of provocation???" Volker tweeted.

Tensions have been building over the Kerch Strait, where Russia has built a new bridge that gives it a land connection to Crimea.

Kiev has accused Moscow of blocking access for Ukrainian ships though the strait, the only way in and out of the Sea of Azov to the Black Sea.

The European Union warned Sunday that tensions in the Azov Sea and Kerch Strait had "increased dangerously" and demanded Russia restore freedom of passage.