Pro-Russian rebels have opened up a new front in south-eastern Ukraine.
Reports say they have taken the town of Novoazovsk, on the Sea of Azov, and are heading for the key port of Mariupol.
Ukraine says Russian forces have crossed the border and are supporting the rebel attack, but the Moscow government has repeatedly denied arming or covertly supporting the rebels.
There are suspicions that Russia wants to divert Ukrainian forces from the besieged cities of Donetsk and Luhansk.
Government forces have made significant advances against the separatists in recent weeks.
German Chancellor Angela Merkel has demanded an explanation from Russia's President Vladimir Putin amid the reports of an incursion.
The US said it suspected a Russian-directed counter-offensive was under way.
Ukrainian forces 'leaving'
Reports from journalists and military on the ground suggest that Novoazovsk had been captured by the rebels.
'The guys from the east shot the positions of the Ukrainian army and the army left Novoazovsk,' freelance journalist Petr Shelomovsky told the BBC.
'Since the morning, they've been leaving the town and we've probably seen the last armoured personnel carrier leaving the place.'
A Ukrainian company commander, Vladimir Shilov, told Ukrainian TV that the town was blocked by tanks and no-one was allowed to leave. Local officials had already fled to Mariupol, he added.
A spokesman for the rebels told Interfax news agency that Novoazovsk was under their control and they would soon 'liberate' Mariupol.
The port has until now been peaceful and cut off from rebel positions.
Rebels have been trying for weeks to break out of an area further north in the Donetsk region where they are almost encircled.
Analysts say the separatists could also be seeking a land link between Russia and Crimea, which also would give them control over the entire Sea of Azov.
Russia annexed the Black Sea peninsula of Crimea from Ukraine in March.
'Military duty'
In a phone call with the Russian president, Mrs Merkel said reports of a Russian military incursion into Ukrainian territory had to be cleared up, her spokesman said.
'The latest reports of the presence of Russian soldiers on Ukrainian territory must be explained,' said Steffen Seibert.
War in eastern Ukraine: The human cost
At least 2,119 people had been killed and 5,043 wounded since mid-April, a UN report on 7 August said 951 civilians have been killed in Donetsk region alone, the official regional authorities said on 20 August Official casualty counts only record certified deaths while in some particularly dangerous parts of the war zone, such as Luhansk region, victims are said to have been buried informally, for instance in gardens Rebels (and some military sources) accuse the government of concealing the true numbers of soldiers killed 155,800 people have fled elsewhere in Ukraine while at least 188,000 have gone to Russia
The US also expressed its 'deep concern' at the latest developments.
'These incursions indicate a Russian-directed counter-offensive is likely under way in Donetsk and Lugansk [Luhansk],' state department spokeswoman Jen Psaki told reporters.
She said Washington had noted 'the Russian government's unwillingness to tell the truth even as its soldiers are found... inside Ukraine'.
Earlier this week, 10 Russian paratroopers were captured on Ukrainian territory 20km (12 miles) from the Russian border.
The Kremlin said the soldiers had entered Ukraine by mistake.
And Denis Pushilin, a rebel leader in Donetsk, denied that Russia was involved in the current offensive.
'If Russia entered into the war the counter-offensive would already be in Kiev. For now, we do without outside help,' he said.
Another rebel leader, Alexander Zakharchenko, insisted that any Russians fighting on the rebel side were doing so voluntarily.
'Many former high-ranking military officers have volunteered to join us. They are fighting with us, considering that to be their duty,' he said.
'There are also many in the current Russian military that prefer to spend their leave among us, brothers who are fighting for their freedom, rather than on a beach.'
Ukrainian President Petro Poroshenko promised a roadmap for peace in the east on Tuesday after holding his first direct talks on the crisis since June with Mr Putin.
Mr Putin said Russia would assist any ceasefire talks, but that stopping the fighting was a matter for Ukraine alone.
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