A NATO military officer told Reuters that "well over 1,000" Russian troops were now operating inside Ukraine on Thursday. Reuters also reported that Finland had accused Russia of violating its airspace for the third time in less than a week.
As a result of the incursion, Ukrainian President Petro Poroshenko cancelled an official visit to Turkey. He said on Twitter:
Also on Twitter, Ukrainian Prime Minister Arseniy Yatsenyuk accused Russia of invading and called on the West to freeze Russian assets until it pulled out of of the country:
Two senior German lawmakers have called for further European Union sanctions against Russia in the light of developments.
Kuleba told CNBC: "We are working on a prompt response and reaction to this flagrant violation of international law and Ukrainian territorial integrity."
"We will defend ourselves, but we will not follow the path that was designed for us by the Russians and we strongly count on the support coming from the European Union and the United States on this particular situation," he added.
The United Nations Security Council will hold an emergency meeting to discuss Ukraine.
Russian stock indexes and the ruble fell sharply on Thursday, on dented hopes of a resolution to the crisis and increased risk of further western sanctions against Russia.
The ruble-denominated MICEX index closed down around 1.7 percent.
European stocks also ended lower on the allegations, with the German DAX—many of whose companies are reliant on Russian gas—hard hit. It closed unofficially lower by 1.2 percent, underperforming the pan-European STOXX 600.
The ruble fell sharply to 36.71 against the U.S. dollar, down 1.5 percent.
Shares in Sberbank, Russia's top bank, closed nearly 6 percent lower, even though it reported results that showed a 13 percent rise in second quarter net profit, beating analysts' forecasts.
The U.S. ambassador to Kiev, Geoffrey Pyatt, tweeted on Thursday:
The accusations follow Tuesday's presidential summit in Minsk between Poroshenko and Russia's Vladimir Putin, which failed to lead to any diplomatic breakthroughs despite discussion of a new ceasefire.
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"We believe that financial markets have become excessively optimistic in the glow of encouraging statements. The fighting appears likely to continue," J.P. Morgan said in a research report.
J.P. Morgan recommended that investors move to underweight positions in Russian and Ukrainian sovereign bonds, arguing that further western sanctions have become more likely given the allegations of Russian regular troops entering Ukraine.
Reuters corrected this story to show that the statement on Ukraine's presidential website referred to Russian troops having been "brought into Ukraine'', not an invasion.