The Russian government denied its troops had entered Ukraine, but the reports risked further inflaming tensions between Moscow and the West which have already imposed costly economic restrictions on each other.
Nato spokeswoman Oana Lungescu said: "If confirmed, they are further evidence Russia is doing the very opposite of what it's saying. Russia has been escalating the conflict, even as it calls for de-escalation."
At a meeting of EU foreign ministers in Brussels, Foreign Secretary Philip Hammond said he was alarmed Russian forces might have crossed the border.
Mr Hammond said: "If there are any Russian military personnel or vehicles in eastern Ukraine, they need to be withdrawn immediately or the consequences could be very serious."
Ukrainian officials said some armoured vehicles did cross from Russia into Ukraine overnight and that they were investigating.
Ukrainian military spokesman Oleksiy Dmytrashkivsky said: "These movements into Ukrainian territory take place practically every day with the aim of provoking (the Ukrainian side)."
Despite the allegations of a fresh Russian military incursion, the momentum on the battlefield in eastern Ukraine is with the government forces.
They are winning territory from the separatists almost daily, and in the main rebel strongholds of Donetsk and Luhansk are pounding the rebels with artillery strikes. Civilians have also been wounded and killed.
The rebels meanwhile appear to be in a disorderly retreat with three senior separatists removed from their post in the past seven days. One of them was Igor Strelkov, a Moscow native so feted among pro-Russian circles that T-shirts and mugs have been printed in Russia with his image.
Western worries about Russian intervention in eastern Ukraine had focused on a huge convoy Moscow said was taking humanitarian supplies to Ukrainian civilians.
Some European officials had said the convoy could be a cover for a Russian military incursion, though Moscow dismissed that.
Russia yesterday let Ukrainian officials inspect an aid convoy and agreed to let the Red Cross distribute the aid around the rebel-held city of Luhansk.
The move helped ease tensions and dispel Ukrainian fears the aid operation is a ruse to get military help to separatist rebels.
Asked about the amount of cargo in the lorries, after it emerged many were only partially filled, a spokesman for the Russian Emergencies Ministry, which is overseeing the convoy, declined to comment.
After the agreement on allowing the lorries access, Ukrainian border guards and customs officials began inspecting the Russian aid at the border crossing.
Laurent Corbaz, the International Committee of the Red Cross' director of operations in Europe, described a tentative plan in which the lorries would enter Ukraine with a single Russian driver each accompanied by a Red Cross worker and with no military escort.