Ukraine's security and defence council said the border town of Novoazovsk and other parts of Ukraine's south-east had fallen under the control of Russian forces who, together with rebels, were staging a counter-offensive. "A counter-offensive by Russian troops and separatist units is continuing in south-east Ukraine," the council said in a post on Twitter.
President Petro Poroshenko, in a statement explaining his decision to cancel a visit to Turkey, said: "An invasion of Russian forces has taken place."
Russia denies intervening in Ukraine by arming the rebels or sending soldiers across the border. The defence ministry declined to comment on reports of Russian tanks in Novoazovsk. "The Russian authorities clearly said many times there are no regular Russian troops there. Russia is not taking part in this armed conflict," said a Russian diplomatic source.
The latest escalation in the five-month crisis came only two days after the presidents of the two countries held their first talks in more than two months and agreed to work towards launching a peace process.
Ukrainian Prime Minister Arseny Yatseniuk appealed to the United States, European Union and G7 countries "to freeze Russian assets and finances until Russia withdraws armed forces, equipment and agents".
Rebel advances this week have opened a new front in the conflict just as Ukraine's army appeared to have gained the upper hand, virtually encircling the separatists in their main strongholds of Donetsk and Luhansk.
Anton Gerashchenko, an adviser to Ukrainian Interior Minister Arsen Avakov, said on Facebook: "The invasion of Putin's regular Russian army of Ukraine is now an established fact!"
French President Francois Hollande said it would be "intolerable and unacceptable" if it was proved true that Russian troops had entered Ukrainian territory.
Tanks in Novoazovsk
The loss of Novoazovsk is a blow to government forces since it leaves vulnerable the big port city of Mariupol, further west along the coast.
A resident who would only give his first name of Mykola, said: "The authorities in the town are DNR (rebel Donetsk People's Republic) ones. Tanks are moving here and there out on the highway, but there is no fighting going on for the town."
A military source said the separatist forces had also taken Savur-Mohyla, a hill east of the city of Donetsk which gives strategic command over large areas of the territory.
Alexander Zakharchenko, prime minister of the self-proclaimed Donetsk People's Republic, told Reuters in an interview that the rebel forces had gained a foothold on the Azov Sea and their objective was to fight their way to Mariupol.
He said there were about 3,000 Russian volunteers serving in the rebel ranks.
The latest developments, and the capture by Ukraine this week of 11 Russian soldiers on its territory, have strained the credibility of Russia's denials that it is sending weapons and soldiers to help the separatists. Russia said the first group of 10 soldiers had probably crossed the border by mistake.
The crisis has prompted Western governments to impose sanctions on Moscow, which has responded in kind, and fanned tensions with NATO to levels not seen since the Cold War.
In a tweet, the U.S. ambassador to Kiev, Geoffrey Pyatt, said: "Russian supplied tanks, armored vehicles, artillery and multiple rocket launchers have been insufficient to defeat Ukraine' armed forces. So now an increasing number of Russian troops are intervening directly in fighting on Ukrainian territory.
"Russia has also sent its newest air defense systems including the SA-22 into eastern Ukraine & is now directly involved in the fighting," he said.
On financial markets, Ukrainian credit default swaps, a form of insurance against the government failing to pay its debt, surged to new three-month highs and dollar bonds fell.
Russia's dollar-denominated RTS share index was down 2.4 percent and the rouble-based MICEX fell 2.1 percent. The rouble also weakened, and Russian debt insurance costs rose to two-week highs.
Fighting in the east erupted in April, a month after Russia annexed Ukraine's Crimean peninsula in response to the toppling of a pro-Moscow president in Kiev.
A United Nations report this week said more than 2,200 people have been killed, not including the 298 who died when a Malaysian airliner was shot down over rebel-held territory in July.