The 10 tanks and two armoured infantry vehicles were said to have crossed the border near Novoazovsk, Ukraine's most south-easterly point on the Azov Sea.
Ukrainian military spokesman Andriy Lysenko said: "This morning there was an attempt by the Russian military to open a new area of military confrontation in the southern Donetsk region."
If the rebels seized control of the southern regions, they could support the separatist stronghold city of Donetsk from the south with easier access to the Russian border.
Fighting between government forces and pro-Russian separatists has been hitherto concentrated around the two big rebel-held cities of Donetsk and Luhansk.
Ukraine has accused Moscow of carrying out regular cross-border shelling of government positions to shore up the rebels who have been increasingly hemmed in by Kiev's forces.
It has also charged Russia with carrying out cross-border incursions involving Russian military to carry out operations in support of the rebels. Moscow denies these charges.
The fresh charges of a blatant Russian military incursion into Ukraine are certain to sour further the atmosphere between the two powers ahead of talks today between Ukrainian President Petro Poroshenko and Russia's Vladimir Putin.
The talks in the Belarussian capital of Minsk, which will also involve leading EU officials, will produce the first encounter since June between the two leaders.
But with Russia blaming the crisis on Ukraine's military offensive and Ukraine refusing to show restraint until Russia halts its support for the rebels, the chances of any breakthrough appear slim.
The new military thrust - whether it is by separatist rebels alone or with the aid of Russian soldiers - might be aimed at capturing Mariupol, a key government-held port city on the Azov Sea.
But Mr Lysenko said the main highway linking Novoazovsk to Mariupol, about 20 miles west along the coastline, was still under the control of government forces.
The commander of a Ukrainian national guard unit in the area near Novoazovsk where the fighting was reported to be happening said: "A war has broken out here." Asked at a news conference in Moscow about reports of an incursion across the border from Russia into the area of Ukraine near Markine, Russian Foreign Minister Sergei Lavrov said: "I have not heard of this but there is plenty of disinformation out there about our 'incursions'."
The separatist rebellions erupted in Ukraine's mainly Russian-speaking east in April after street protests ousted a Moscow-backed president in February.
When leaders with a pro-Western agenda took power in Kiev, Russia annexed Crimea and Mr Putin spoke of Russia's right to defend the interests of Russian speakers in Ukraine.
The UN say more than 2,000 people - Ukrainian service personnel, civilians and rebels - have been killed in the conflict.
The Ukrainian military said the total number of its forces killed stood at 726, with four more service personnel killed yesterday.