The two Russian frigates -- the Admiral Makarov and the Admiral Grigorovich -- had earlier left the port of Sevastopol on the peninsula of Crimea, which Russia annexed from Ukraine in 2014, and were transitting the Bosphorus and then the Dardanelles straits.

A Russian military spokesman insisted that the transit was a routine move, despite the timing and the fact the two heavily armed frigates passed simultaneously.

"The frigates Admiral Makarov and Admiral Grigorovich -- armed with highly accurate Kalibr-NK missile systems -- are carrying out a planned transit from Sevastopol," fleet spokesman Alexei Rulev told the RIA Novosti and Interfax news agencies.

He did not specify where the ships were eventually heading, but Russian naval ships that pass through the Bosphorus normally head into the Mediterranean to back Moscow's operations in Syria.

The transit came hours after Ankara announced at least 33 Turkish soldiers were killed in Syria's Idlib province after a strike it blamed on Russia's ally Damascus.

Russia said the troops were "where they should not have been" and had been among "terrorists".

The incident has raised new questions about the sustainability of the alliance between Turkey and Russia to bring peace to Syria.

As a Black Sea littoral state, Russia is allowed to have its military ships pass through the Bosphorus under the 1936 Montreux Convention on the Straits.

Under its terms, Turkey can only block Russian naval shipping if war is declared or if it feels under an imminent threat of war.

The deputy head of the Russian lower house of parliament's defence committee, Yuri Shvytkin, warned Turkey against closing the Bosphorus saying that "Ankara now needs to refrain from aggressive plans, military actions and rhetoric," Interfax reported.

But an influential member of the Russian upper house's defence committee, Frants Klintsevich, said he did not believe there would be any fighting between Turkish and Russian forces.

A spokesperson for the Russian embassy in Ankara meanwhile told Interfax that the mission and other Russian representations had been given additional security by the Turkish authorities.