"Ukrainian soldiers captured two armoured vehicles of Russia's Pskov Airbourne division in a battle near Lugansk," said security spokesman Andriy Lysenko at a briefing.
"One of the vehicles had a full set of documents, from driver's licenses to military documents," he said, adding that the vehicles had been abandoned by their drivers.
Ukrainian journalist Roman Bochkala, who is travelling with Kiev's army in the Lugansk region, published pictures on his Facebook page claiming to show a vehicle with its plates scratched out and various items apparently found inside, including a Russian passport.
Russia swiftly rejected allegations that it had sent vehicles into Ukraine.
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"Among the daily 'exposure' of Russian presence in Ukraine this is the 1001st such piece of 'evidence'," military spokesman Igor Konashenkov told Russian state agency ITAR-TASS.
He said that Ukraine's army has the same equipment and the documents allegedly found inside had been stolen.
Kiev has accused Russia of sending weapons and soldiers into eastern Ukraine to aid the rebels as it mounts an offensive to surround Donetsk and Lugansk and cut off the area from the Russian border.
The 76th Chernigov airborne assault division based in Pskov, a city in western Russia close to the borders with Estonia and Latvia, is Russia's oldest paratrooper unit.
It participated in various conflicts and peacekeeping missions in the former Soviet Union and beyond, as well as Russia's war in Chechnya.
In February, Pskov lawmaker Lev Shlosberg wrote in a blog that the division has been sent to Crimea, where days later soldiers appeared armed to the teeth but without any identifying insignia.
The so-called "little green men" helped to seize Ukrainian military bases in the peninsulaafter a hastily organised referendum led to its annexation by Russia.