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Nearly all Russian forces that had been staged along the border with Ukraine have been withdrawn and returned to their usual bases of operation, U.S. defense sources told NBC News.

Only 2,000 of the estimated 40,000 Russian military forces that had been poised at the border now remain at the forward staging area. Russia has also withdrawn most of its heavy equipment, including tanks and attack helicopters.

The United States had feared the large number of Russian forces within a few miles of the border made it possible for Russia to launch an invasion into Ukraine with practically “no warning,” and repeatedly demanded those forces be withdrawn to reduce regional tensions.

This week, Ukrainians elected Petro Poroshenko as the country's president and Russia said it would respect the vote.

The Associated Press contributed to this report.