A senior Ukrainian official has said two columns of Russian tanks and military vehicles fired at a border post, before entering the southeast of the country.
The comments by Col. Andriy Lysenko, a spokesman for Ukraine's National Security Council, followed Ukrainian President Petro Poroshenko's assertion that Russian forces had "entered" the country.
It is reported the tanks moved into an area of the eastern Donetsk region which was seized by the separatists for the first time earlier this week.
They now control the southeastern town of Novoazovsk and have threatened to take the strategic port city of Mariupol, marking a new front in the conflict which has claimed more than 2,100 lives since April.
According to the Interfax news agency, Mr Poroshenko said Russian troops had come "to the rescue" of pro-Moscow separatists battling Ukrainian forces.
A Nato official, meanwhile, said at least 1,000 Russian troops had entered Ukraine with sophisticated equipment and had been in "direct contact" with Ukrainian forces resulting in casualties.
The reports support claims from the West and Kiev that Russia is operating in the east of the country.
Satellite image provided by the Supreme Headquarters Allied Powers Europe
Ukraine's Prime Minister Arseniy Yatsenyuk accused Russian President Vladimir Putin of having "deliberately unleashed a war in Europe".
In a statement, Prime Minister David Cameron said he is "extremely concerned by mounting evidence that Russian troops have made large-scale incursions into southeastern Ukraine, completely disregarding the sovereignty of a neighbour.
"The international community has already warned Russia that such provocative actions would be completely unacceptable and illegal."
He called on Russia to immediately cease all military activity in Ukraine or face "further consequences."
A Ukrainian serviceman exchanges fire with rebels
Moscow has consistently denied arming the rebels and sending troops across the border.
Responding to the latest allegations, the Defence Ministry said reports of the presence of Russian military vehicles in Ukraine bore "no relation to reality."
The UN Security Council is to hold an emergency meeting to discuss the crisis today, while Nato is due to hold a separate emergency meeting on Friday.
German Chancellor Angela Merkel said an EU summit on Saturday would discuss the prospect of further sanctions on Russia in light of the latest reports and has demanded an explanation.
Russian paratroopers captured in Ukraine on Monday
French President Francois Hollande has said it would be "intolerable and unacceptable" Russian forces they were involved in any fighting.
Mr Poroshenko has cancelled a working trip to Turkey and called an emergency meeting of Ukraine's security and defence council.
Earlier the defence council said Ukrainian government forces had withdrawn from Novoazovsk "to save their lives" and were now reinforcing troops in the port city of Mariupol.
On Wednesday a top rebel leader, Alexander Zakharchenko, admitted Russian troops were fighting alongside his insurgents, but said they were on "holiday" after volunteering to join the battle.
Mr Putin and Mr Poroshenko at the talks in Minsk on Tuesday
Zakharchenko, prime minister of the self-proclaimed Donetsk People's Republic, told Reuters there were about 3,000 Russian volunteers serving in the rebel ranks.
The spiralling tensions come two days after Mr Poroshenko and Mr Putin held their first talks in three months and agreed to work towards launching a peace process.
The day before Ukraine captured 10 Russian paratroopers around Amvrosiivka, a town about 12 miles (20km) from the border with Russia.
The Russian stock market dived on Thursday amid fears grew the country was escalating its role in the five-month conflict, with the MICEX index dropping nearly two percent.