Ukrainian border guards retreated Thursday as two columns of Russian tanks streamed into the nation, prompting fears that Russia is creating a land link between its territory and Crimea.

Ukrainian security council spokesman Col. Andriy Lysenko says Ukrainian forces were fired at using Grad missile systems from Russian territory at about 11 a.m.

Lysenko said about an hour and a half later, two columns -- including tanks and other fighting vehicles -- began an attack on a border post.

They later entered Ukraine from Veselo-Voznesenka and Maximovo of the Rostov region in Russia.

Ukrainian border guards retreated because they didn't have heavy equipment.

The incursion reported Thursday continues several weeks of Russian military action in Ukraine. Tanks, armor and soldiers have been streaming across the border, and on Thursday, NATO released several images from last week that show purported Russian tank columns.

"This is like watching a frog boil," a Pentagon official told Fox News. "They turn up the heat."

Meanwhile, a Russian separatist said Thursday that there were up to 4,000 Russian troops in Ukraine.

"We have never hidden from anybody (the fact) there are many Russians among us," Alexander Zakharchenko, the prime minister of the self-proclaimed Donetsk Poeple's Republic, said at a press conference. "Without their help it would be very difficult for us to fight."

Brig. Gen. Nico Tak, a top NATO official, told reporters at NATO headquarters that the ultimate aim of Russia was to stave off defeat for the separatists and turn eastern Ukraine into a "frozen conflict" that would destabilize the country "indefinitely."

NATO estimated that another 20,000 Russian troops were right over the Russian border.

Tak said the 1,000 Russian troops operating inside Ukraine was a conservative estimate and provided satellite imaginary showing an incursion of great sophistication. He refused to specify exactly what the "contact" with Ukrainian troops was.

A leader of pro-Russian rebels in eastern Ukraine reportedly has admitted that thousands of Russians have been fighting alongside his troops.

Alexander Zakharchenko told Russian television that he estimated that between 3,000 and 4,000 Russians had joined the ranks, and claimed that they were either former Russian service members or current military personnel on leave, according to the BBC. However, he also insisted that any Russians who went to flight did so voluntarily and not on orders from superiors in Moscow.

Russia's ambassador to the EU, Vladimir Chizhov, told the BBC that "NATO has never produced a single piece of evidence" of Russian troops operating in Ukraine. He said the only Russian soldiers in Ukraine were the 10 captured this week, who Moscow insists had mistakenly wandered across the border.

The Russian Defense Ministry didn't directly deny its troops were in Ukraine, but said the list of Russian military units said to be operating in Ukraine had no relation to reality.

U.S. officials tell Fox News that they believe that Russian special forces are fighting in Ukraine, with one saying "if you look at a Russian separatist, it is basically a Russian soldier."

A senior U.S. defense official also told Fox News that the Pentagon has seen evidence that Russia has fired artillery inside Ukrainian territory at Ukraine military positions in recent days.

"This is not the first time," the official said. However, U.S. officials are not ready to declare that Russia has begun invading Ukraine.

U.S. Ambassador to Ukraine Geoffrey Pyatt posted the following statement in three Twitter messages Thursday: "Russian supplied tanks, armored vehicles, artillery and multiple rocket launchers have been insufficient to defeat Ukraine's armed forces. So now an increasing number of Russian troops are intervening directly in fighting on Ukrainian territory. Russia has also sent its newest air defense systems including the SA-22 into eastern Ukraine & is now directly involved in the fighting."

Ukraine and its Western allies have repeatedly accused Russia of providing weapons and training to the rebels, who declared independence from Kiev in two eastern districts this past April following Russia's annexation of the Crimean peninsula. Moscow, in turn has repeatedly denied the accusations.

Joseph Dempsey, an analyst at the International Institute for Strategic Studies in London, said recent images of a military convoy in eastern Ukraine showed the presence of a variant of the T-72 tank which "is not known to have been exported or operated outside of Russia."

The tanks' presence, he added in a blog published Thursday, "strongly supports the contention that Russia is supplying arms to separatist forces."

Zakharchenko's admission that Russians had joined the ranks came as the rebels appeared to have captured the strategic town of Novoazovsk in southeastern Ukraine. On Thursday morning, an Associated Press journalist saw rebel checkpoints at the outskirts and was told he could not enter. One of the rebels said there was no fighting in the town.

Novoazovsk, which lies along the road connecting Russia to the Crimean peninsula, had come under shelling for three days, with the rebels entering on Wednesday.

The southeastern portion of Ukraine along the Azov Sea previously had escaped the fighting engulfing areas to the north. The loss of Novoazovsk could open the way for the rebels to advance on the much larger port of Mariupol.

The new southeastern front raises fears that the separatists are seeking to create a land link between Russia and Crimea. If successful, it could give them or Russia control over the entire Sea of Azov and the gas and mineral riches that energy experts believe it contains. Ukraine already has lost roughly half its coastline, several major ports and significant Black Sea mineral rights in March when Russia annexed Crimea.

President Petro Poroshenko announced in a statement published online Thursday that he was canceling a visit to Turkey for the inauguration of newly elected president Recep Tayyip Erdogan and called a snap session of Ukraine's security council.

"I have decided to cancel my visit to Turkey because of the sharp escalation of the situation in the Donetsk region... as Russian forces have entered Ukraine," he said.

"Destabilization of the situation and panic, this is as much of a weapon of the enemy as tanks," Poroshenko told the security council, according to the Interfax news agency.

U.N. Undersecretary-General of Political Affairs Jeffrey Feltman opened a meeting of the U.N. Security Council Thursday telling members the latest developments mark a "dangerous escalation in the conflict."

Power reminded the council that the meeting was "the 24th session to try to rein in Russia's aggressive acts in the Ukraine."

"Every single one has sent a straightforward, unified message: 'Russia, stop this conflict. Russia is not listening,'" she said, adding that Russia's force along the border is the largest it's been since it started deploying in late May.

State Department spokeswoman Jen Psaki said Thursday that Moscow is engaged in a "pattern of escalating aggression in Ukraine," now including combat forces, armored vehicles, artillery and surface-to-air missiles.

Psaki added that the U.S. could increase economic sanctions against Russia. But she said no such decisions have been made. And to help Ukraine, she said Washington is focused on nonlethal forms of assistance and not military equipment.

Also on Thursday, a pro-government militia fighter told Reuters that in addition to taking Novoazovsk, the rebels had captured a strategic hill just east of Donetsk, one of two major rebel strongholds that Ukrainian forces had surrounded in recent weeks.

The recent reversals by Kiev's forces have prompted claims from Ukraine that Russian forces have crossed the border in an effort to open a new front and prevent pro-government forces from dealing a decisive blow to the rebels in Donetsk and Luhansk.

In Donetsk, 11 people were killed by shelling during the night, the city administration said in a statement.

Fox News' Jennifer Griffin and The Associated Press contributed to this report.

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