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WASHINGTON — The Pentagon phoned the Russian Defense Ministry within the past 24 hours to say Defense Secretary Chuck Hagel is willing to talk directly with his Russian counterpart at any time. The Russians have not returned the call.

The revelation is seen as a sign that the U.S. is growing increasingly concerned that Russian troops are about to invade Ukraine.

Defense officials say Hagel again wanted to appeal to Russian Defense Minister Sergei Shoigu to help “de-escalate the crisis in Ukraine.” And to re-iterate that Russian actions so far have had a “destabilizing effect that is not helpful.”

U.S. officials tell NBC News that Russian forces “pulsing the border” with Ukraine have been operating in small battalions, several hundred soldiers with armored vehicles and attack helicopters.

Russian servicemen drive armoured personnel carriers on the outskirts of the city of Belgorod near the Russian-Ukrainian border, April 25, 2014.STRINGER / Reuters

According to the officials, the Russian forces advance on Ukraine, but stop short close to the border, then turn either north or south to continue along the border for several miles before returning to their garrisons.

Defense Department officials also confirmed that Russian fighter jets flew into Ukrainian airspace a handful of times over the last 24 hours. The jets performed no threatening maneuvers during the flyovers, the officials said.

The officials say it appears there are three objectives to the maneuvers: training, intimidation and intelligence gathering — the latter to gauge the response from Ukrainians across the border.

There is also the possibility that the exercise itself could be used as a feint to mask an actual invasion.

Officials say there is still no sign they Russian forces are falling into large formations for an actual invasion.

But defense officials have repeatedly said that from their current positions, the Russians could launch an invasion within 12 hours.

— Jim Miklaszewski and Courtney Kube