The Ukrainian military says it has clashed with rebel armoured vehicles that crossed from Russia and headed to the south-eastern port of Mariupol.
One commander said rebels might be trying to open up a new southern front. Russia did not comment on the issue.
Ukrainian President Petro Poroshenko voiced his "extreme concern" about the alleged crossing, his office said.
More than 2,000 people have died in fighting between Ukrainian forces and the separatists in recent months.
Some 330,00 people have been displaced.
Mr Poroshenko made the comments during a telephone conversation with EU Council President Herman Van Rompuy, his office said.
He was reacting to Russian Foreign Minister Sergei Lavrov, who said the Kremlin planned to send a second humanitarian convoy "in the next few days" as the situation there was "deteriorating".
The first convoy, which returned at the weekend, crossed the border without Ukraine's authorisation. Ukraine feared it was carrying military equipment to pro-Russian separatists and denounced it as an invasion.
Mr Lavrov also said he had not heard the reports about the alleged incursion into Ukraine, but complained of regular "disinformation about our 'incursions'".
The Russian and Ukrainian presidents are scheduled to meet in Minsk, Belarus, on Tuesday for talks on the crisis.
Ukraine's military said border guards had halted the column about 5km (3 miles) north-east of Novoazovsk, which is about 10km from the frontier in the far south-east of Ukraine.
Heavy clashes were reported at the village of Markyne.
One commander of a Ukrainian national guard unit in the area told Reuters news agency: "A war has broken out here."
Ukraine's National Security and Defence Council later said in a statement that two tanks were destroyed and several members of a "sabotage and reconnaissance" group were seized.
It said the area was blocked by Ukrainian troops.
Ukrainian sources earlier said the armoured vehicles had crossed the border bearing symbols of the self-styled Donetsk People's Republic.
Officials said 10 tanks and two armoured personnel carriers were in the column although other reports said the number of vehicles was as high as 50.
Mariupol, a major port on the Azov Sea, is in the hands of Ukrainian government forces, who ousted rebels from the city in June after weeks of fighting.
A Ukrainian military spokesman said government forces still controlled Mariupol and the road to Novoazovsk.
Spokesman Andriy Lysenko said it was an attempt "by the Russian military in the guise of Donbas fighters (rebels) to open a new area of military confrontation". The scene of most of the fighting has been much further north.
Mr Lysenko said there were enough resources to repel any attack.
Ukraine and Western powers have accused Russia of arming the rebels, charges Moscow has denied.
There have been numerous previous reports of armoured vehicles crossing Ukraine's eastern border.
Mr Lavrov said he had also sent a note to the Ukrainian foreign ministry on Sunday informing it of the new aid convoy.
"The humanitarian situation is not improving but deteriorating," he said.
"We want to reach an agreement on all conditions for delivering a second convoy by the same route... in the coming days".
Russia said the first convoy had delivered generators, food and drink.
Asked about Tuesday's presidential meeting, Mr Lavrov said: "We are ready... for any format as long as there is a result," adding that Russia wanted "to help Ukrainians agree among themselves".
Mr Lavrov also commented on the parading of captured Ukrainian government soldiers by rebels through the centre of Donetsk on Sunday.
Crowds lined the streets chanting "fascists" as the dishevelled-looking prisoners walked by.
Mr Lavrov said this was "nowhere near mistreatment" and that Ukrainian fighters' actions often amounted to "war crimes".
"I saw images of that parade and I didn't see anything close to what could be considered as humiliating," he said.
The violence in east Ukraine erupted in April when pro-Russian separatists in the Donetsk and Luhansk regions declared independence from Kiev. This followed Russia's annexation of the Crimean peninsula from Ukraine in March.