Russian President Vladimir Putin on Sunday raised the stakes in the Ukraine conflict by calling for the first time for statehood to be discussed for the restive east of the former Soviet state.

The remarks came just hours after the European Union gave Moscow -- which the bloc accuses of direct involvement in the insurgency -- a week to change course or face new sanctions.

"We need to immediately begin substantive talks... on questions of the political organisation of society and statehood in southeastern Ukraine," the Russian leader was quoted by Russian news agencies as saying.

Moscow has previously only called for "federalisation" that would grant greater rights to the eastern regions of Ukraine, where predominantly Russian-speakers live.

But Putin had sparked speculation that he may be seeking to create a pro-Russian statelet when he began to employ the loaded Tsarist-era term "Novorossiya", or New Russia, to refer to several regions in southeast Ukraine.

His spokesman Dmitry Peskov said Sunday that the Russian leader was not talking about "Novorossiya's" independence from Ukraine, but rather "inclusive talks".

"Only Ukraine can agree with Novorossiya," he was quoted as saying.

Kiev has warned that it was on the brink of "full-scale war" with Moscow over the crisis in its east, which Europe fears would put the whole continent at risk of conflict.

The EU agreed to take "further significant steps" if Moscow did not rein in its support for the rebels, with new sanctions to be drawn up within a week.

Kiev said the invigorated rebel push of the past days has included substantial numbers of Russian regular army contingents, which are now concentrating their forces in major towns.

"Terrorists and Russian soldiers continue to concentrate personnel and equipment in regional centres," said security spokesman Andriy Lysenko.

AFP correspondents in the town of Komsomolske, south of rebel hub Donetsk, saw rebels tinkering with abandoned Ukrainian armoured personnel carriers.

"We arrived this morning, there was no fight," a rebel nicknamed "Shatun" (a bear awakened from hibernation), told AFP.

Soviet-made T-64 assault tanks seen by AFP near Starobesheve, a town about 30 kilometres southeast of Donetsk siezed by the rebels, had only one number to mark them out, at the back, while fighters wore unmarked fatigues.

One pro-Russia rebel perched on the side of a tank, however, was decisive that they were not taken from the Ukrainians.

"No, they are ours," he told AFP, before being hushed by his comrade, who added quickly: "Yes, we took them from the Ukrainians."

'Today Ukraine, tomorrow Europe'

NATO last week accused Moscow of sending at least 1,000 troops across the border to fight alongside the rebels, along with artillery, tanks and armoured vehicles.

Lithuania's President Dalia Grybauskaite, whose Baltic nation is wary of the resurgent power on its eastern border, warned that "Russia is practically in a state of war against Europe" and called for EU military assistance to Kiev.

Over 2,600 people have died in the Ukraine conflict since mid-April.

Ukrainian President Petro Poroshenko urged Brussels to take tougher steps against Russia's "military aggression and terror" and warned that a "full-scale war" with Moscow is closer than ever.

"Today we are talking about the fate of Ukraine, tomorrow it could be for all Europe," he said.

Poroshenko said he expected the West to ramp up its arms supplies to Ukraine after discussions at a NATO summit in Wales on Thursday and Friday, where he is expected to meet with US President Barack Obama.

Moscow denies direct involvement in the conflict, but there have been media reports of secret military funerals for those sent to fight in Ukraine.

Russia admitted that Russian paratroopers had been captured in Ukraine, but alleged they crossed the border by accident.

Last city standing

Rebels have pushed a lightning offensive around Ukraine's Azov Sea in the past week, prompting speculation of a possible attempt by Moscow to establish a corridor between Russia and the Crimean peninsula it annexed in March.

The rebels have advanced swiftly along the coast, capturing the town of Novoazovsk last Wednesday, just one day after Poroshenko met with Putin for talks that failed to achieve any breakthrough.

Ukraine's border guard service said its two ships were fired upon off the Azov Sea coast close to the city of Mariupol, though could not confirm reports that the attack came from Russian airforce.

Mariupol "is the last big town in the region under Ukrainian control, home to half a million people," commander of Ukraine's Azov battalion, Andriy Biletskiy told AFP.

Inside the strategic port, volunteer battalions were bracing for a desperate defence of the city, manning barricades of barbed wire and trenches.

"We can hold them off, but for how long? We don't have the strength to beat them," said "Panther", a tattooed fighter with the Azov battalion, said to be one of the most radical nationalist groups in the area.

Alexander Zakharchenko, prime minister of the self-proclaimed Donetsk People's Republic, spoke to Russian media Saturday about "preparing a second large-scale offensive".