Petro Poroshenko’s 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 UN Security Council is to hold an emergency meeting in New York on August 28 at 18:00 GMT to discuss the crisis.
NATO Brigadier General Niko Tak said 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 defense systems, artillery, tanks, and armored 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 favoring 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.
However, 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.
On August 28, 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 between 3,000 and 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 defense 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 defenses of the strategic port city of Mariupol.
The port has until now been peaceful and cut off from rebel positions.
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.
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