NOVOAZOVSK, Ukraine -- Two columns of tanks and military vehicles rolled into southeastern Ukraine from Russia on Thursday after Grad missiles were fired at a border post and Ukraine's overmatched border guards fled, a top Ukrainian official said.

Echoing the comments by Ukrainian Col. Andriy Lysenko, a senior NATO official said at least 1,000 Russian troops have poured into Ukraine with sophisticated equipment, leaving no doubt that the Russian military had invaded southeastern Ukraine.

"The hand from behind is becoming more and more overt now," Brig. Gen. Nico Tak said at NATO's military headquarters, adding that Russia's ultimate aim was to stave off defeat for the separatists and turn eastern Ukraine into a "frozen conflict" that would destabilize the country indefinitely.

"An invasion is an invasion is an invasion," tweeted the Lithuanian ambassador to the UN, Raimonda Murmokaite.

The UN Security Council will hold an emergency meeting on Thursday afternoon.

"Russian forces have entered Ukraine," Ukrainian President Petro Poroshenko said, cancelling a foreign trip and calling an emergency meeting of the country's security council. "Today the president's place is in Kyiv."

Poroshenko urged his citizens to resist giving into panic.

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

As Poroshenko spoke, the strategic southeastern town of Novoazovsk appeared firmly under the control of separatists and their Russian backers, a new, third front in the war in eastern Ukraine between the separatists and Poroshenko's government in Kyiv.

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 Defence 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.

Lysenko said the missiles from Russia were fired at Ukrainian positions in the southeast about 11 a.m. and an hour and a half later, two columns, including tanks and other fighting vehicles, began an attack. They entered Ukraine from Veselo-Voznesenka and Maximovo in the Rostov region of Russia.

Russian stock markets dived as Switzerland joined the European Union in imposing restrictions on Russian state banks and fears grew that the U.S. and EU could impose further sanctions on Russian businesses and individuals in response to the military escalation. Russia's MICEX index dropped nearly 2 per cent on Thursday, and major Russian state banks VTB and Sberbank dropped more than 4 per cent.

"Over the past two weeks we have noted a significant escalation in both the level and sophistication of Russia's military interference in Ukraine," Tak said in Casteau, Belgium. "Russia is reinforcing and resupplying separatist forces in a blatant attempt to change the momentum of the fighting, which is currently favouring the Ukrainian military."

He said the 1,000 Russian troops was a conservative estimate and said another 20,000 Russian troops were right over the border.

NATO also produced satellite images to provide what it called additional evidence that Russian combat soldiers, equipped with sophisticated heavy weaponry, are operating inside Ukraine's sovereign territory.

"This is highly sophisticated weaponry that requires well-trained crews, well-trained command and control elements, and it is extremely unlikely that this sort of equipment is used by volunteers," Tak said.

Moscow has described the Russian citizens fighting with the separatists as volunteers.

Tak said the satellite images were only "the tip of the iceberg" in terms of the overall scope of Russian troop and weapons movements.

NATO also has detected large quantities of advanced weapons, including air defence systems, artillery, tanks and armoured personnel carriers being transferred to separatist forces in eastern Ukraine," he said. "The presence of these weapons along with substantial numbers of Russian combat troops inside Ukraine make the situation increasingly grave."

The leader of the insurgency, Alexander Zakharchenko, said in an interview on Russian state television Thursday up to 4,000 Russians have fought on the separatist side since the armed conflict began in April.

The U.S. government also has accused Russia of orchestrating the rebel campaign and sending in tanks, rocket launchers and armoured vehicles.

"These incursions indicate a Russian-directed counteroffensive is likely underway in Donetsk and Luhansk," U.S. State Department spokeswoman Jen Psaki said. She voiced concern about overnight deliveries of materiel in southeast Ukraine near Novoazovsk and said Russia was being dishonest about its actions, even to its own people.

Russian forces, she said, are being sent 30 miles (about 50 kilometres) inside Ukraine, without them or their families knowing where they are going. She cited reports of burials in Russia for those who have died in Ukraine and wounded Russian soldiers being treated in a St. Petersburg hospital.

On Thursday morning, an Associated Press journalist saw rebel checkpoints on Novoazovsk's outskirts and was told he couldn't enter. One of the rebels said there was no fighting in the town.

Novoazovsk, which lies along the road connecting Russia to the Russia-annexed Crimean Peninsula, had come under shelling for three days, with the rebels entering it on Wednesday. This area had previously escaped the fighting that has engulfed areas to the north, and the only way rebels could have reached the southeast was by coming through Russia.

The new southeastern front raised 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 lost roughly half its coastline, several major ports and significant Black Sea mineral rights in March when Russia annexed Crimea.

In Mariupol, a city of 450,000 about 30 kilometres (20 miles) to the west of Novoazovsk, a brigade of Ukrainian forces arrived at the airport on Wednesday, while deep trenches were dug a day earlier on the city's edge.

National Guard spokesman Ruslan Muzychuk told the AP in Mariupol that the government has evidence that large amounts of weapons have been brought into Novoazovsk from across the Russian border.

He added that National Guard reinforcements were taking up positions in Mariupol.

"The positions are being strengthened," the spokesman said. "The road from Novoazovsk to Mariupol is under the control of Ukrainian troops."

Associated Press journalists on the border have seen the rebels with a wide range of unmarked military equipment -- including tanks, Buk missile launchers and armoured personnel carriers -- and have encountered many Russians among the rebel fighters.

In Donetsk, the largest rebel-held city, 11 people were killed by shelling overnight, the city said Thursday.