"The battle between Ukrainian paratroopers and a reinforced tank battalion of the Russian armed forces is continuing with the goal of controlling the Lugansk airfield," military spokesman Leonid Matyukhin wrote on his Facebook page.
Ukraine's Defence Minister Valeriy Geletey further said that Russian units are moving into other towns in the region, including the largest city of the region Donetsk.
"The information that Russian troops are there has been confirmed," he said.
"We are fighting Russia and it is Russia which is deciding what will happen in Donbass," he told Ukraine's Inter channel late Sunday, referring to the informal name of the Donetsk and Lugansk regions.
"We are holding talks not with terrorists but with representatives of the Kremlin," he added.
Pro-Russian rebels in eastern Ukraine have in recent days seized large swathes of territory, with Kiev saying the offensive has been reinforced with a larger than ever influx of Russian weaponry and troops.
NATO accused Moscow of sending 1,000 regular troops across the border, a large part of which is no longer controlled by Kiev.
Moscow has denied sending soldiers into Ukraine, saying paratroopers detained by Kiev about 20 kilometres from the Russian border got there by accident.
Fighting between Kiev's army and the insurgency has killed over 2,600 people since mid-April.
Also on Monday Russia's Foreign Minister Sergei Lavrov said a meeting of the Ukraine Contact Group in Minsk should discuss an immediate and unconditional ceasefire.
"I am very much counting upon the negotiations set for today, to above all focus on agreeing an immediate and unconditional ceasefire," he said a meeting with university students according to Russian news agencies.
Representatives of Kiev, Moscow and the OSCE are to meet Monday in Minsk, but it was unclear if representatives of pro-Russian separatists would attend.