WASHINGTON (Reuters) - Russia’s reinforcement of troops near Ukraine has brought the total forces there to as many as 40,000, U.S. officials estimated on Friday, as the United States voiced anxiety over the buildup and called on Moscow to pull back its military.

The U.S. estimates of as many as 35,000 to around 40,000 troops are higher than the more than 30,000 total deployments reported earlier this week by U.S. and European sources familiar with official reporting.

Some European sources remain cautious of increasing the estimates beyond 30,000.

The military buildup is adding to concerns that Russia may again be readying an incursion into Ukraine following its annexation of Crimea, which has triggered the worst stand-off with the West since the Cold War.

“The possibility of another Russian incursion is very real,” a U.S. intelligence official said, echoing increasingly ominous statements by other Obama administration officials.

The Russian deployments included the establishment of supply lines and the fielding of a wide range of military forces, U.S. officials say, speaking on condition of anonymity.

These include militia or special forces units made up of Russian fighters wearing uniforms lacking insignia or other identifying markings, similar to the first Russian forces to move into Crimea during Russia’s recent military takeover there, according to U.S. and European sources familiar with official reporting.

The Pentagon has said there was no indication that the forces were carrying out the kind of springtime military exercises Moscow has officially cited as the reason for their deployment.

U.S. President Barack Obama on Friday described the buildup as out of the ordinary.

“You’ve seen a range of troops massing along that border under the guise of military exercises,” he said on CBS “This Morning” in Vatican City. “But these are not what Russia would normally be doing.”

Obama said the moves might be no more than an effort to intimidate Ukraine, but could be a precursor to other actions.

“It may be that they’ve got additional plans,” he said in excerpts from an interview with CBS “Evening News,” to be broadcast in full on Friday night.

Ukraine’s government has put its heavily outnumbered and outgunned forces on alert for an invasion from Russia in the east, following Moscow’s takeover of Crimea, as the West moves to isolate Russia diplomatically and pressure it economically.

Sailors stand next to a weapons system onboard a Russian Navy vessel anchored at a navy base in the Ukrainian Black Sea port of Sevastopol in Crimea, March 28, 2014. REUTERS/Yannis Behrakis

Ukraine's estimates of Russian forces near the border are far higher than Western figures, with Ukrainian security chief Andriy Parubiy citing nearly 100,000 troops on Thursday, via webcast from Kiev to a U.S. think tank. His comments can be seen here: here

Exactly what Russian President Vladimir Putin plans to do with his forces on the Ukraine border is not known, U.S. officials said.

Some officials say intelligence information available to policymakers regarding what Putin is thinking, and what he is saying to his advisers and military commanders, is fragmentary to non-existent.

Putin has reserved the right to send troops into Ukraine, the eastern part of which is home to a large population of Russian-speakers. On Friday, he said Russia’s takeover of Crimea showed off its military prowess.

“The recent events in Crimea were a serious test,” Putin was shown saying on state television.

“They demonstrated both the completely new capabilities of our Armed Forces and the high morale of the personnel.”