Russia has "well over a thousand", a senior Nato official said on Thursday.
The official, who was quoted by the Financial Times, said the supply of arms by Russia had increased in both "volume and quality" and the latest developments in Ukraine "have made clear that the security paradigm in Europe has fundamentally changed" as Russia has become "very aggressive".
Earlier on Thursday, Ukrainian officials said Russian forces had entered the country and helped local separatists capture the coastal town of Novoazovsk in south-eastern Ukraine.
Ukrainian president Petro Poroshenko said in a televised statement from Kiev on Thursday that he had convened an emergency meeting with his military chiefs as "the introduction of Russian forces into Ukraine has taken place".
He also called for an emergency meeting of the United Nations Security Council and the European Council.
Pro-Russian rebels have been reinforced by Russian army forces in skirmishes near Luhansk and Ilovaisk, according to the Kiev Post, quoting a report by the information and analytical center of the Ukrainian National Security and Defense Council (NSDC).
The Latvian foreign ministry said that reports of the appearance of Russian troops on Ukrainian territory were a sign of the beginning of full-scale "war", while Lithuania called the attack an "obvious invasion of the territory of Ukraine by the armed forces of the Russian Federation".
A military source was earlier quoted by Reuters as saying that pro-Russian forces had taken control of Savur-Mohyla, a hill to east of the city of Donetsk, a site of strategic importance as it offers control on large parts of the surrounding areas.
"There is military equipment in Novoazovsk which came across the border two days ago from Russia," a militant of the Azov battalion, which supports the Ukrainian army, told Reuters.
"The equipment is carrying the flags of the DNR (Donetsk People's Republic) rebels but they are regular Russian forces."
Over the past two weeks, Ukrainian forces had made steady progress in the eastern part of the country and had successfully managed to isolate the two rebel strongholds of Luhansk and Donetsk, but the latest development is a blow to Kiev's military.
"Russian supplied tanks, armoured 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," said Geoffrey Pyatt, the US ambassador in Ukraine.
"Russia has also sent its newest air defence systems including the SA-22 into eastern Ukraine & is now directly involved in the fighting."
Ukraine's Foreign Ministry used Twitter on Wednesday evening to bring attention to what it called an invasion, using a pair of hashtag, #UkraineUnderAttack and #RussiaInvadedUkraine, urging users on the social network to share the message.