Newspaper the Guardian said Friday its reporter saw several armored personnel carriers, or APCs, cross the border with Ukraine.
The newspaper said the move was unlikely to represent a full-scale official Russian invasion, but it was clear evidence that Russian troops are active inside Ukraine's borders.
Dozens of heavy Russian military vehicles massed on Friday near the border with Ukraine, where a huge Russian convoy with humanitarian aid came to a halt as Moscow and Kiev struggled to agree on border crossing procedures.
Another reporter working for Reuters said he saw two dozen APCs moving near the border with Ukraine on Thursday night.
Russia says it is carrying 2,000 tons of water, baby food and other aid for people in east Ukraine, where pro-Moscow separatists are fighting government forces.
Kiev and some Western officials have said they believe the convoy could be a cover for a Russian military incursion, a claim Moscow has described as "absurd."
On Thursday, the convoy of some 280 trucks stopped in open fields near the Russian town of Kamensk-Shakhtinsky, about 20 kilometers from the border with Ukraine.
Kiev and NATO have said they fear Russia will invade east Ukraine after massing more than 40,000 troops near the border. Russia says it is conducting military exercises and has no plans to invade. It also denies supporting rebels in eastern Ukraine with arms and funds.
Kiev has said if the humanitarian convoy enters Ukraine without the consent of the authorities, the Ukrainian government would view that as an illegal Russian incursion, further heightening tension.
However, there is still a possibility that a deal could be brokered. Russia's foreign ministry said it was in intensive negotiations with the Ukrainian government and the Red Cross.
A senior official of the Red Cross arrived in Kiev on Thursday for talks on aid.
Relief agencies say people living in Luhansk and in Donetsk face shortages of water, food and electricity after four months of conflict, in which the UN says more than 2,000 people have been killed.
Kiev blames Russia and the separatists for the plight of the civilians, but their situation has grown more acute as the Ukrainian military has pressed its offensive —including in areas where civilians live.
Artillery shells hit close to the centre of Ukraine's separatist-held city of Donetsk for the first time on Thursday.