Russian troops have arrived in eastern Ukraine hours after President Vladimir Putin announced that he would recognize the independence of two separatist regions, European officials said Tuesday morning.

"Russian troops have entered in Donbas," the name for the area where the two separatist regions, Donetsk and Luhansk, are located, European Union foreign policy chief Josep Borrell said in Paris. "We consider Donbas part of Ukraine."

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When asked whether Putin's decision to order Russian troops into the regions amounts to an invasion, Borrell said, "I wouldn’t say that’s a fully-fledged invasion, but Russian troops are on Ukrainian soil."

A woman holds her dog as she waits with others to cross from Ukrainian government controlled areas to pro-Russian separatists' controlled territory in Stanytsia Luhanska, the only crossing point open daily, in the Luhansk region, eastern Ukraine, Tuesday, Feb. 22, 2022. (AP Photo/Vadim Ghirda)

Poland's Defense Ministry and British Health Secretary Sajid Javid also said Russian forces had entered Ukraine's east. Javid went further, telling Sky News that "the invasion of Ukraine has begun."

"We are waking up to a very dark day in Europe and it’s clear from what we have already seen and found out today that the Russians, President Putin, has decided to attack the sovereignty of Ukraine and its territorial integrity," Javid said.

Russian officials haven't yet acknowledged any troop deployments to the rebel east, but Vladislav Brig, a member of the separatist local council in Donetsk, told reporters that the Russian troops already had moved in, taking up positions in the region's north and west.

In the hours after Russia said it was sending what it deems "peacekeepers" into eastern Ukraine, convoys of armored vehicles were seen rolling across the separatist-controlled territories on Monday night. It wasn’t immediately clear if they were Russian.

In this image provided by the United Nations, the U.N. Security Council meets for an emergency session on Ukraine, Monday, Feb. 21, 2022, at the U.N. headquarters. (Evan Schneider/United Nations via AP)

With an estimated 150,000 Russian troops massed on three sides of Ukraine, the U.S. has warned that Moscow has already decided to invade. Still, President Biden and Putin tentatively agreed to a meeting brokered by French President Emmanuel Macron in a last-ditch effort to avoid war.

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Ukraine President Volodymyr Zelenskyy continues to downplay concerns of a potential Russian invasion of his country, but suggested on Tuesday that Ukraine could cut off diplomatic ties with Moscow.

Meanwhile, EU foreign ministers have planned a meeting Tuesday to decide what sanctions to impose over Russia’s decision to recognize two separatist regions in eastern Ukraine.

The Associated Press contributed to this report.