The Ukrainian military says it is battling rebel armoured vehicles that crossed from Russia and headed to the south-eastern city of Mariupo, reports GHN based on BBC.
It said the column was halted near the town of Novoazovsk.
One military commander said pro-Russian rebels might be trying to open up a new southern front.
Russian Foreign Minister Sergei Lavrov said he not heard the reports but complained of regular "disinformation about our 'incursions'".
He also said Russia planned to send another humanitarian convoy into eastern Ukraine "in the next few days" as the humanitarian situation there was "deteriorating".
Its first convoy, which returned at the weekend, crossed the border without Ukraine's authorisation. Ukraine feared the convoy was carrying military equipment to the pro-Russian separatists and denounced it as an invasion.
More than 2,000 people have died in recent months in fighting between Ukrainian government forces and the separatists. Some 330,00 people have been displaced.
The Russian and Ukrainian presidents are scheduled to meet in Minsk, Belarus, on Tuesday for talks on the crisis.