The Interfax news agency quoted Arsen Avakov as saying that a "column" with armored vehicles crossed from Russia through border control points controlled by pro-Russian separatists near the Dyakove village in eastern Ukraine.
He said vehicles including automobiles and armoured personnel carriers crossed the border. He said that three tanks went to the town of Snizhne about 40 kilometres from Dyakove. One remained there while two others left in the direction of the town of Horlivka and were engaged by the Ukrainian military.
Russia has denied sending troops or equipment into Ukraine and no independent confirmation was immediately available.
Avakov said the incursion took place despite Russian statements of interest in a peaceful solution and intent to increase border controls.
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The reports followed statements earlier today by Russia's foreign minister that the pro-Moscow separatist rebels in eastern Ukraine are ready for a cease-fire but that Kiev has to initiate the process.
Sergey Lavrov also was quoted by Russian news agencies as saying Moscow will introduce a resolution in the United Nations on the Ukrainian crisis, but that Russia was not seeking authorisation to send in peacekeeping troops. The Ukrainian rebels have suggested that Russia should send peacekeepers, but Moscow says that could only be done with UN authorisation.
Lavrov said that "We know that the rebels in the southeast are ready to hold fire, but the first step by all rights should be made by the Kiev authorities.