Ukrainian forces prepare for an advance to Mariupol in south-east Ukraine. 27 Aug 2014 Ukrainian forces are being deployed to help defend the southern city of Mariupol
German Chancellor Angela Merkel has demanded an explanation from Russia's President Vladimir Putin amid reports that Russian troops have launched an incursion into south-east Ukraine.
Ukraine said Russian forces had crossed the border and were supporting separatist attacks.
The US State Department said it suspected a Russian-directed counter-offensive was under way.
Russia has repeatedly denied arming or covertly supporting the rebels.
The BBC's Barbara Plett Usher in Washington says the suspicion is that Moscow is opening a new front to divert Ukrainian forces from the besieged cities of Donetsk and Luhansk, where they have made significant advances against pro-Russian separatists.
However, Denis Pushilin, a rebel leader in Donetsk, told a news conference that Russia was not 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.
He added that the rebel forces were receiving more volunteers, some from as far away as Serbia.
Earlier on Wednesday, the mayor of the Ukrainian port of Novoazovsk on the Sea of Azov said rebel tanks and armoured vehicles had entered the town.
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.
The reports of renewed fighting came just hours after Ukrainian President Petro Poroshenko promised a roadmap for peace in the east.
He spoke after holding his first direct talks on the crisis since June with Putin.
In a phone call with the Russian president, 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.
"She [Mrs Merkel] emphasised Russia's major responsibility for de-escalation and watching over its own frontiers."
The Kremlin confirmed the phone call but gave no details.
A senior Nato diplomat said Russian support for the separatists was becoming increasingly open.
The diplomat, speaking to reporters in Brussels on condition of anonymity, said: "I think there's a shift here that we may be witnessing, very recently, from largely covert, ambiguous, deniable support to what appears increasingly to be flat-out, overt and obvious (support) and with the only form of ambiguity being that the Russians... claim it is not happening."
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.
The mayor of Novoazovsk, Oleg Sidorkin, told the Associated Press news agency on Wednesday that rebels had penetrated the town and he had seen "dozens" of tanks and armoured vehicles roll in.
Ukraine insisted it was still in control of the town but said seven villages to the north had been captured by separatists.
Novoazovsk is in the south of Donetsk region, near the port city of Mariupol where Ukrainian security forces dislodged rebels in June.
After his meeting with Poroshenko on Tuesday, Putin said Russia would assist any ceasefire talks, but that stopping the fighting was a matter for Ukraine alone.