Ukraine has charged two suspected Russian soldiers, who were captured during a gun battle in the separatist eastern region of Lugansk, with involvement in "terrorist activity," a security official said Wednesday.

Ukrainian Security Service spokesman Markiyan Lubkivsky wrote on Facebook that Captain Yevgeny Yerofeyev and Sergeant Aleksander Aleksandrov, now convalescing in a Kiev military hospital, were also allowed to telephone their relatives in Russia.

Moscow has said that the two men were once members of the Russian armed forces but had been demobilized by the time they crossed into the Ukrainian war zone nearly two months ago.

The men are alleged to have testified during a taped interrogation that they were members of a 200-strong Russian reconnaissance unit that entered the war zone nearly two months ago.

Moscow acknowledges the presence of Russian "volunteers" and off-duty servicemen in Ukraine, while rejecting charges that they were there under orders from President Vladimir Putin's generals.

Ukrainian President Petro Poroshenko believes the men's capture further boosts his claim of the Kremlin's direct involvement in the 13-month separatist uprising, which the United Nations believes has claimed more than 6,250 lives.

A top Ukrainian security official said on Tuesday that the men would put on a "public" trial and released if they confessed to being members of the Russian armed forces and that they were ordered to fight alongside the separatists.

The Russian army on Monday demanded the prisoners' immediate release and promised to open direct talks over the men's fate with the Ukrainian security service.

It is not clear whether such talks are currently being held.