Ukraine said on Friday it had destroyed part of a Russian military convoy that crossed onto its territory in an incursion that has sent cross-border tensions rocketing.

NATO accused Russia of active involvement in the "destabilisation" of eastern Ukraine, where pro-Kremlin separatists have been fighting against Kiev for four months.

The two countries have also been wrangling for days over a Russian convoy that Moscow says is carrying aid for besieged rebel-held cities but which Kiev suspects could be a "Trojan horse" to provide military help to the insurgents.

Fears that the border clash could spill into all-out war between Kiev and Moscow sent major share markets tumbling across Europe and the United States.

Ukrainian President Petro Poroshenko told British Prime Minister David Cameron that government artillery had destroyed a "considerable part" of a small military convoy that entered the country, the presidency said in a statement.

The European Union demanded that Russia "put an immediate stop to any form of border hostilities, in particular to the flow of arms, military advisers and armed personnel into the conflict region, and to withdraw its forces from the border."

French President Francois Hollande called on Russia to respect Ukraine's territorial integrity and for both sides to try to de-escalate the "very high tensions," while Britain summoned Moscow's ambassador to "clarify" the situation and a spokesman for Cameron said Russia needs to show "a willingness to find a peaceful solution to the conflict".

Moscow's defence ministry dismissed the alleged convoy as a "phantom", its latest denial of Western accusations that it is funnelling weapons to the pro-Russia separatists who launched an insurgency against Kiev in April.

"Such statements, based on fantasies... should not be a subject of serious discussion for leaders of any country," spokesman Igor Konashenkov told Russian news agencies.

But NATO chief Anders Fogh Rasmussen backed reports of the "Russian incursion" after British media said it had seen the convoy of some 20 vehicles cross the border.

"It just confirms the fact that we see a continued flow of weapons and fighters from Russia into the eastern Ukraine," he said.

"It is a clear demonstration of continued Russian involvement in the destabilisation of eastern Ukraine."

As the fallout snowballed, Ukraine's foreign minister announced he will meet his Russian counterpart Sergei Lavrov in Berlin on Sunday for talks alongside the top diplomats from France and Germany.

"Be it a square table or a round one, we need to talk," minister Pavlo Klimkin wrote on Twitter.

- 'Attempts to derail aid' -

Russia's foreign ministry ominously accused Ukraine of "attempts to derail the supply of humanitarian aid" as doubts swirled over what will happen next to almost 300 Russian trucks parked up some 30 kilometres (20 miles) from Ukraine's border.

Moscow accused Kiev of stepping up military operations with the "obvious goal" of blocking the agreed route.

It had appeared earlier that the two countries might reach a deal to allow the convoy into Ukraine to help people in the east who are without water, food or power.

But the International Committee of the Red Cross said they were still ironing out details over the shipment.

"People are struggling to cope with limited access to basic services such as water and electricity, so speed is of the essence," said Laurent Corbaz, ICRC head of operations for Europe and Central Asia.

Ukraine fears the convoy could be used as a pretext to invade, as a pro-Moscow rebellion shows signs of unravelling after four months of fighting that has left more than 2,000 people dead including children and sent around 285,000 fleeing their homes.

Moscow has insisted the white-tarpaulin trucks are hauling aid and officials tried to prove that by showing off the contents of 10 lorries with baby formula, rations and bottled water to journalists.

"We've shown you everything. You see that we have nothing to hide -- these trucks are carrying nothing but humanitarian aid," said Sergei Karavaytsev, from Russia's emergency situations ministry.

- Kiev pushes on offensive -

Meanwhile Ukraine said it was forging on with an offensive that has sent rebel forces reeling, retaking three small towns overnight.

Top rebel military chief Igor Strelkov and another key commander announced Thursday they were quitting after Ukraine's military said it had completely surrounded Lugansk, cutting all links to the border with Russia.

The head of the self-proclaimed Donetsk People's Republic, Alexander Zakharchenko, described the situation in rebel-held areas as "critical" and demanded that Russian aid be let in.

An AFP journalist in the main rebel-held city of Donetsk in the industrial heartland of eastern Ukraine heard sporadic shelling from a suburb and saw rebels driving howitzer cannons into the city centre.

The death toll continues to climb, with mortar fire in Donetsk killing 11 civilians over the past 24 hours, local authorities said. Five soldiers were also killed in fighting over the same period.

As the Russian aid sat at the border, Ukrainian officials said their own aid convoys -- some 75 lorries with 800 tonnes of aid -- had arrived at a government-held town some 100 kilometres north of Lugansk.