DONETSK, Ukraine — The warnings from the North Atlantic Treaty Organization and the White House over the past week could not have been graver in tone: The Russian Army, they said, had massed enough forces on the border with Ukraine to invade.

The last time Russian troops appeared to menace Ukraine, in the spring, the Ukrainian military quickly halted attacks on pro-Russian separatists to avoid the chance of touching off a new war in Europe. Not this time.

Buoyed by successes against the separatists over the past two months — and noting that the Russians have threatened an invasion in the region before without following through — Ukrainian commanders have pressed ahead with an offensive to drive the rebels from their stronghold in Donetsk in the east.

The army continued to fire artillery into the city nightly, and paramilitary groups raided outlying villages despite warnings from President Vladimir V. Putin of Russia that he could intervene at any time to protect Ukrainians who favor closer ties with his country. And the Ukrainians have flaunted their victories.
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Some of the only backers of the notion that Mr. Putin will surely not invade appear to be the pro-Russian separatists in Ukraine who crave his help. Yuri, a commander of about 500 pro-Russian fighters defending Donetsk, said he does not believe the Russians will cross the border.

“Russia,” he said, “is afraid of starting World War III.”

For the moment, it is clear the Ukrainians are emboldened.
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Officials in Kiev say the militias and the army coordinate their actions, but the militias, which count about 7,000 fighters, are angry and, at times, uncontrollable. One known as Azov, which took over the village of Marinka, flies a neo-Nazi symbol resembling a Swastika as its flag.

In pressing their advance, the fighters took their orders from a local army commander, rather than from Kiev. In the video of the attack, no restraint was evident. Gesturing toward a suspected pro-Russian position, one soldier screamed, “The bastards are right there!” Then he opened fire.