The Russian soldiers were captured with documents and weapons on them, the Security Service said.
Russia has repeatedly denied claims by Kiev that it has sent troops and weapons over the border into Ukraine, where the Ukrainian military is fighting pro-Russia rebels.
Russia's state-run RIA Novosti news agency cited a source in the Russian Defense Ministry as saying the soldiers had been patrolling the border and "most likely crossed by accident" at an unmarked point.
The development comes as Ukrainian President Petro Poroshenko and his Russian counterpart, Vladimir Putin, prepare to meet for the first time since June.
The two leaders are in Minsk, the capital of Belarus, for trade talks related to the Eurasian Customs Union, a trade bloc made up of Russia, Belarus and Kazakhstan.
Senior European Union officials, headed by EU foreign policy chief Catherine Ashton, are also in Minsk for the talks.
"The EU is attending to see if discussions can help create momentum for a new political solution to the crisis in Ukraine," said Ashton's spokeswoman, Maja Kocijancic.
It's not yet been confirmed whether Putin and Poroshenko, who last met briefly during D-Day commemorations in France, will hold bilateral talks in Minsk.
But Russian Foreign Minister Sergey Lavrov did not rule out the possibility Monday, saying: "Russia is ready to take part in the Ukrainian crisis settlement in any format that might lead to their national unity."
The current conflict was first sparked last year by a political crisis over whether Ukraine would seek closer ties with Europe or with Russia. The ouster of pro-Moscow President Viktor Yanukovych in February was followed by Russia's annexation of Ukraine's Crimea region in March and a declaration of independence by separatist leaders in the Donetsk and Luhansk regions.
Poroshenko in June signed a landmark EU trade pact, despite opposition from Russia.
Poroshenko's trip to Belarus comes a day after he announced that he had dissolved the nation's parliament, with elections scheduled for October 26.
Meanwhile, fighting continues for control of the cities of Luhansk and Donetsk, both strongholds for the rebel fighters.
Ukraine accuses Russia of fomenting the crisis by backing the rebels, a claim Moscow denies. Russia, meanwhile, says Ukraine's assault against the rebels is precipitating a humanitarian crisis.
The besieged city of Luhansk has been without water and power for over three weeks, city officials said Sunday. Shelling has caused major damage there and in surrounding villages over past weeks.
Members of the Mahounin family told CNN how they fled their town two days earlier. Intense shelling meant they'd had to spend 24 hours a day in an underground bomb shelter with more than 100 others.
"I don't care what they're fighting for, I just want to survive -- I want my son to survive," said Lilia Mahounin.
Lavrov told reporters that Russia hopes to send a second humanitarian aid convoy to Ukraine this week to help civilians caught up in the conflict.
Last Friday, a convoy of 227 Russian trucks crossed that country's border into eastern Ukraine without Kiev's authorization, a move condemned by international powers as a violation of Ukraine's sovereignty. Officials in Kiev referred to it as an invasion.
The trucks left a day later, having successfully delivered supplies to Luhansk, Russian authorities said. Ukrainian authorities said they suspected the delivery had been used to bolster rebel forces.
The International Committee of the Red Cross is struggling to get desperately needed aid to civilians in besieged towns and cities because of the volatile security situation.
"We have 10 trucks full of humanitarian goods that we want to bring in, but so far, there was no possibility to bring that in because of security reasons," an ICRC official, Peter Huber, told CNN.
U.N. officials estimate that more than 2,000 people have died and nearly 5,000 have been wounded in eastern Ukraine since mid-April.
German Chancellor Angela Merkel, on a weekend visit to Kiev, promised Ukraine loans worth 500 million euros to help rebuild shattered infrastructure and homes.
Determined to preserve the pro-Russian revolt in eastern Ukraine, Russia reinforced what Western and Ukrainian officials described as a stealth invasion on Wednesday, sending armored troops across the border as it expanded the conflict to a new section of Ukrainian territory.
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