"The Ukrainian border has been breached by a convoy of several dozen tanks and armoured vehicles" which crossed in the area close to Ukraine's industrial city Mariupol, security spokesman Leonid Matyukhin told AFP.
"The convoy has been stopped by border guards... The battle is ongoing," he said, without providing any other details.
Mariupol, a coastal city of 500,000 on the Azov Sea in the southern Donetsk region, is located about 50 kilometres (30 miles) from the Russian border and some 110 kilometres from the rebel-controlled Donetsk.
It is the heart of eastern Ukraine's metals industry and home to one of the biggest metals factories in eastern Ukraine.
The city participated in the referendum on May 11 on breaking off from Kiev's authority to become an independent "Donetsk people's republic," but has been in control of Kiev's forces for months.
Pitched battles in the city on May 9 killed more than a dozen people, with the army ousting pro-Russian rebels several days later.
Since then Mariupol has been the seat of the pro-Kiev Donetsk regional governor and administration, which left Donetsk after separatists took control.
The regional authorities on Monday issued a message appeared aimed at stopping panic in the city, stressing that both the governor and the administration are "functioning as usual" and not fleeing their offices.
