Ukrainian President Petro Poroshenko has said Russian troops have been "brought into Ukraine" and has called an urgent meeting of security and defence council to decide the next steps in order to resolve the crisis.
"I made the decision to cancel a working visit to the Republic of Turkey in connection with the rapidly deteriorating situation in Donetsk region, in particular in Amvrosiyivka and Starobesheve, as Russian troops have actually been brought into Ukraine," Poroshenko said in a statement on the presidential website.
US President Barack Obama told a news conference in Washington on Thursday that violence in eastern Ukraine was being "encouraged by Russia", adding that pro-Russian separatists fighting Ukrainian troops were also receiving training from Moscow.
Samantha Power, the US ambassador to the UN which discussed the violence in an emergency meeting, said Russia should "stop lying and fuelling this conflict".
"At every step Russia has come before this [Security] Council to say everything except the truth. It has manipulated, it has obfuscated, it has outright lied," Samantha told the Security Council.
David Cameron, the British prime minister, said Russia must stop its tanks from entering Ukraine, warning that Moscow - already reeling from sanctions imposed by the EU and the US - would face further consequences if a political solution to the crisis was not found.
"It is simply not enough to engage in talks in Minsk [the capital of Belarus], while Russian tanks continue to roll over the border into Ukraine. Such activity must cease immediately," Cameron said in a statement on Thursday.
NATO confirmed on Thursday that at least 1,000 Russian troops were on Ukrainian territory.
Russian Ambassador to the UN Vitaly Churkin said Russian troops fighting alongside pro-Russian separatists were "volunteers", and accused Washington of backing Ukraine militarily.
Earlier, a pro-Russia rebel leader said serving Russian soldiers, on leave from their posts, were fighting Ukrainian troops alongside the country's separatists in eastern Ukraine, the website of a Russian state television channel has reported.
"Among us are fighting serving soldiers, who would rather take their vacation not on a beach but with us, among brothers, who are fighting for their freedom," said Zakharchenko in an interview posted on Thursday on Vesti.ru.
Al Jazeera's Paul Brennan, reporting from eastern Ukraine, said the crisis had entered a new and "dangerous territory".
"No longer are we talking about rumours of Russian involvement with separatist fighters. There have been outright accusations and backed up apparently by clear-cut satellite image evidence that Russian regular forces are fighting alongside separatist fighters," he said.
"The Russian side for its part has been ... denying any Russian regular troops are here ... but, frankly, the evidence is mounting, and quite how long the Russians can continue to deny what is increasingly becoming undeniable is really a moot point."
As the Security Council debated the crisis, two columns of tanks and military vehicles rolled into southeastern Ukraine from Russia after Grad missiles were fired at a border post and Ukraine's overmatched border guards fled, a top Ukrainian official said.
Echoing the comments by Ukrainian Colonel Andriy Lysenko, a senior NATO official said at least 1,000 Russian troops had poured into Ukraine with sophisticated equipment, leaving no doubt that the Russian military had invaded southeastern Ukraine.
"The hand from behind is becoming more and more overt now," Brigadier General Nico Tak said at NATO's military headquarters.
He said Russia's ultimate aim was to stave off defeat for the separatists and turn eastern Ukraine into a "frozen conflict" that would destabilise the country indefinitely.
"An invasion is an invasion is an invasion," tweeted the Lithuanian ambassador to the UN, Raimonda Murmokaite.
Poroshenko urged his citizens to resist giving into panic.
"Destabilization of the situation and panic, this is as much of a weapon of the enemy as tanks," Poroshenko told the security council.
As he spoke, the strategic southeastern town of Novoazovsk appeared firmly under the control of separatists and their Russian backers, a new, third front in the war in eastern Ukraine between the separatists and Poroshenko's government in Kiev.