Ukraine said ten Russian paratroopers had been captured and has released video interviews of some of the men. One is quoted as saying “this is not our war”.
The incident comes ahead of a key meeting between the Ukrainian and Russian presidents.
Ukraine’s President Petro Poroshenko and his Russian counterpart Vladimir Putin are at a summit in Minsk in Belarus.
More than 2,000 people have died in months of fighting between Ukrainian forces and separatists in the Donetsk and Luhansk regions.
The two regions declared independence from Kiev following Russia’s annexation of the southern Crimean peninsula from Ukraine in March.
A Russian defense ministry source was quoted by the Russian news agency RIA Novosti as saying: “The soldiers really did participate in a patrol of a section of the Russian-Ukrainian border, crossed it by accident on an unmarked section, and as far as we understand showed no resistance to the armed forces of Ukraine when they were detained.”
The source also said that some 500 Ukrainian servicemen had crossed the border at various times, adding: “We did not give much publicity to that. We just returned all those willing to return to Ukrainian territory at safe places.”
Ukraine’s security service said its military had captured the 10 Russian paratroopers near the village of Dzerkalne, about 30 miles south-east of the rebel-held city of Donetsk and about 15 miles from the Russian border.
Ukrainian military spokesman Andriy Lysenko said: “This wasn’t a mistake, but a special mission they were carrying out.”
A Ukrainian television report that carried the interviews with the men said they were from the 331st regiment of the 98th Svirsk airborne division.
It quoted one man, named as Sgt Andrei Generalov, as saying: “Stop sending in our boys. Why? This is not our war. And if we weren’t here, none of this would have happened.”
Another man, named as Ivan Milchakov, says he is based in the Russian town of Kostroma.
“I did not see where we crossed the border. They just told us we were going on a 70km march over three days,” he said.
“Everything is different here, not like they show it on television. We’ve come as cannon fodder.”
Russia has repeatedly denied Ukrainian and Western accusations that it is supporting the rebels.
On Monday, Ukraine said an armored column had crossed the border into south-eastern Ukraine, sparking clashes near Novoazovsk.
The summit in Minsk is also being attended by senior officials from the European Union which, along with the US, has imposed sanctions on Russia for failing to rein in the separatists.
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