Ukraine's President Petro Poroshenko has accused Russia of deploying its troops in the east of his country.
His remarks came as pro-Russian rebels opened a new front in the south by seizing the coastal town of Novoazovsk.
Nato says it has detected a significant increase of Russian arms being supplied to the rebels over the past two weeks.
Russia has denied that its forces have crossed Ukraine's border. At least 2,119 people have been killed in four months of fighting.
The United Nations Security Council is to hold an emergency meeting in New York on Thursday at 18:00 GMT to discuss the crisis.
Nato Brigadier General Niko Tak told the BBC that there had been a "significant escalation in the level and sophistication of Russia's military interference in Ukraine" over the past two weeks.
"[Nato has] detected large quantities of advanced weapons, including air defence systems, artillery, tanks, and armoured personnel carriers being transferred to separatist forces in eastern Ukraine," he said.
"Russia is reinforcing and resupplying separatist forces in a blatant attempt to change the momentum of the fighting, which is currently favouring the Ukrainian military."
More than 1,000 Russian troops are operating inside Ukraine, both supporting the separatists and fighting on their side, according to Nato.
But Russia's ambassador to the EU, Vladimir Chizhov, said Nato had "never produced a single piece of evidence" for its accusations. He said the only Russian soldiers on Ukrainian soil were 10 paratroopers captured earlier this week.
In international reaction:
- British Prime Minister David Cameron warned that if Russia failed to find a political solution to the crisis, "she should be in no doubt that there will be further consequences"
- Polish Foreign Minister Radoslaw Sikorski called the deployment of Russian troops an "aggression" and said international action was needed
- German Chancellor Angela Merkel demanded an explanation from Russian President Vladimir Putin amid the reports of an incursion
- French President Francois Hollande said it would be "intolerable" if Russian troops were in Ukraine, and demanded that Russia stop sending aid to the rebels
On Thursday, Ukrainian President Petro Poroshenko called an emergency meeting with his security council to discuss "the sharp aggravation of the situation in Donetsk region... as Russian troops were actually brought into Ukraine".
"The situation is extremely difficult, but it is manageable enough for us not to panic and continue calculating our actions," he told security chiefs.
Meanwhile Prime Minister Arseny Yatsenyuk said Russia had "unleashed a war in Europe", adding that the world should take "effective steps".
Government forces had made significant advances against the separatists in recent weeks, but these gains seem in doubt with rebels now operating in two distinct areas of Donetsk region.
Separatist leader Alexander Zakharchenko told Russian TV that 3-4,000 Russian citizens were fighting in their ranks.
He said many of the Russians were former service-people or current service personnel on leave, insisting that all were volunteers.
Ukraine's security and defence council confirmed reports that Novoazovsk had been captured by the rebels, whom they described as "Russian troops".
It said it had withdrawn its forces to save lives, and that Ukrainian soldiers were now reinforcing the defences of the strategic port city of Mariupol.
The port has until now been peaceful and cut off from rebel positions.
Keir Giles, analyst, Conflict Studies Research Centre, Oxford
President Vladimir Putin received authorisation from parliament to use troops in Ukraine in March. But in June, during an easing of tension, he asked for that authorisation to be revoked.
The statements that the Russian soldiers in eastern Ukraine are "volunteers" and "on leave" both add a layer of implausible deniability, and get around Russia's own constitutional and legal safeguards against sending servicemen abroad without the proper authority.
Meanwhile, Russia's next steps are an open question. One concern is that the more direct involvement of Russian troops may create the conditions for a "humanitarian intervention" by Russia, using "peacekeepers".
Pro-Russian fighters 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 would give them control over the entire Sea of Azov.
Russia annexed the Black Sea peninsula of Crimea from Ukraine in March.
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