Ukraine said 10 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.
Petro Poroshenko and 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.
`Cannon fodder`
A Russian defence 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 50km (30 miles) south-east of the rebel-held city of Donetsk and about 25km from the Russian border.
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.
`No magic solution`
The BBC`s David Stern in Kiev says Tuesday`s talks in Minsk are under the auspices of the Moscow-led Eurasian Customs Union, which also includes Belarus and Kazakhstan, and that it is still unclear whether Mr Putin and Mr Poroshenko will meet separately.
The gulf between the positions of Ukraine and Russia is huge. Russia wants an unconditional ceasefire in eastern Ukraine. But Ukraine has the upper hand against the rebels there and does not want to simply stop and let them regroup.
Russia stresses that Ukraine must talk to the rebels, but Ukraine says the rebels are not a force of their own - rather an extension of Russia`s hostilities, and it is Russia that must talk to the rebels and persuade them to lay down their weapons.
What will bridge this gulf after so many months of fighting remains unclear.
The pair last met briefly in June at the D-Day commemorations.
The summit in Minsk will also be 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.
Ahead of the talks, Russian Foreign Minister Sergei Lavrov said the West should not put all the onus on Moscow.
"I hope very much our Western colleagues... won`t just come with expectations we will somehow magically solve things for them. That will not work," he told a news conference.
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