Ukraine said Tuesday that fighting had erupted in the heart of the major rebel stronghold of Lugansk as government forces pressed on with a punishing offensive to win back the war-torn east.

Kiev's military claimed street battles with insurgents were raging in the city center after one outlying district was "liberated".

A Moscow court on Monday jailed three activists for up to three-and-a-half years as it wrapped up an explosive two-year trial that put 13 behind bars for protests over Vladimir Putin's presidential return.

The May 2012 clashes between protesters and police spelled a bloody end to months of unprecedented street discontent with Putin's decision to swap his prime minister's seat with then-president Dmitry Medvedev and extend his dominance over Russia by at least six more years.

Ukraine on Monday accused pro-Russian rebels of killing dozens of civilians fleeing the war-torn east, as crisis talks between Kiev and Moscow failed to halt months of bloodshed.

Kiev's military said insurgents using Russia-supplied weapons shelled adults and children in a convoy with white flags on a road from the restive city of Lugansk, leading to "dozens of dead".

Russian Foreign Minister Sergei Lavrov said Monday that no progress was reached on establishing a ceasefire or starting peace negotiations over Ukraine during crisis talks in Berlin with his counterpart from Kiev.

"One place where we cannot report positive results is in, first and foremost, establishing a ceasefire and (starting) a political process," Lavrov told a Berlin press conference that was carried live by Russian state television.

Ukrainian forces battled into a key rebel bastion as fresh claims that rocket launchers had crossed over from Russia stoked tensions Sunday ahead of talks between Kiev and Moscow's top diplomats.

The foreign ministers of Russia, Ukraine, Germany and France gathered for a snap meeting in Berlin, after Western leaders had scrambled frantically to contain the crisis in Ukraine.

European leaders on Saturday scrambled to ease tensions over claims that Ukrainian forces had destroyed Russian military vehicles as Kiev inched closer to allowing a mammoth aid convoy from Moscow over its border.

While a diplomatic push sought to defuse the rhetoric, deadly shelling pummeled besieged pro-Russian rebel strongholds and a top separatist leader claimed he had received a fresh injection of troops trained "on Russian territory."

Diplomatic efforts to douse an international firestorm over claims that Ukraine's forces destroyed Russian military vehicles ratcheted up Saturday as Moscow demanded that Kiev allow its mammoth aid convoy to cross the volatile border.

Moscow and Kiev's foreign ministers prepared for an urgent meeting with their French and German counterparts Sunday after the United States blasted Russia for its "extremely dangerous" escalation of the crisis in Ukraine.

German Chancellor Angela Merkel urged Russian President Vladimir Putin to "stop the flow of military equipment, military advisers and armed personnel crossing the border with Ukraine," in a telephone call on Friday. 

The head of the self-proclaimed Donetsk People's Republic, Alexander Zakharchenko, said Friday that the inhabitants desperately need Russian humanitarian aid and accused Ukraine of deliberately stalling its arrival.

"At the moment, the Donetsk people's republic has a very bad humanitarian situation and the help that Russia is sending us and we have still not received, we just need it like air," Zakharchenko said at a briefing in Donetsk.

Two men lift the tarp of a Russian truck near the border with conflict-ridden Ukraine, showing the cargo to around 25 journalists with cameras and microphones in hand.

"What a lot of journalists for sacks of sugar," mutters the driver, Alexander, whose truck is one of 280 that Moscow says are loaded with humanitarian aid.