By Julian E. Barnes and Anton Troianovski       April 29, 2016

Western allies are preparing to put four battalions—a force of about 4,000 troops—in Poland and the Baltic countries as part of an effort by the North Atlantic Treaty Organization to reinforce its border with Russia as Moscow steps up military activity, officials said Friday.

The U.S. is likely to provide two battalions, while Germany and Britain would likely provide a battalion each, according to Western officials.

U.S. Deputy Secretary of Defense Robert Work, visiting Brussels, confirmed the overall size of the force and said the buildup was a response to more Russian activity around the Baltics—Lithuania, Latvia and Estonia—where tensions have been rising.

“The Russians have been doing a lot of snap exercises right up against the borders, with a lot of troops,” Mr. Work said in an interview. “From our perspective, we could argue this is extraordinarily provocative behavior.”

Russian officials have repeatedly said their own buildup and exercises are a response to NATO’s troop buildup and aggressive posture to Moscow.

NATO defense ministers in February approved in principle the deployment of an Eastern European troop presence, though diplomats said the new contribution numbers aren’t finalized. NATO’s military arm, the Supreme Headquarters Allied Powers Europe, has sent the recommendations to the alliance headquarters in Brussels, where they are being reviewed.

NATO officials want to make sure the force is multinational and are asking smaller allies to make contributions, such as logisticians, for supporting forces.

The participation of a sizable German force is particularly important, alliance officials have said, to creating an effective deterrent against Russia and cement Berlin’s emerging role as a bigger player in NATO.

Germany had been cautious about the troop presence on the eastern border of NATO. The move is unlikely to be popular at home where attitudes to the military are still shaped by post-World War II pacifism. But Chancellor Angela Merkel and her top officials have been making the case for more German engagement on international security matters, arguing the country’s safety and export-driven economy depend on global stability.

German officials said Friday they were considering plans ahead of a NATO summit in Warsaw in July to lead a battalion to be based in Lithuania, but a final decision hadn’t been reached.

“We are currently reviewing how we can continue or strengthen our engagement” on the alliance’s eastern periphery, Ms. Merkel said Friday.

During his recent trip to Germany, President Barack Obama discussed with Ms. Merkel the German contribution, according to German and U.S. officials.

Gregor Gysi, a prominent far-left lawmaker, slammed the German government, saying that the move would send the wrong message on the eve of the 75th anniversary in June of Nazi Germany’s invasion of the Soviet Union.

“To send troops to the Russian border now is to forget history and to escalate,” Mr. Gysi said in a statement.

A Bertelsmann Foundation poll published last week found that just 31% of Germans would support sending German troops to defend the Baltic states or Poland against an attack from Russia. About half of Germans oppose setting up NATO bases in eastern members of the alliance to deter Russia, the poll found, while 40% said they would support such a move.

“We aren’t passive observers and we take all necessary military measures to compensate for such a reinforced and absolutely unjustified military presence,” Alexander Grushko, Russia’s envoy to NATO, said in a statement.

The U.K. Ministry of Defense declined to comment, but a British official said no final decisions have been made on deploying U.K. troops to the region.

Mr. Work said the precise U.S. contribution was still being discussed. But other officials said the U.S. was discussing sending two battalions. The U.S. battalions are likely to be drawn from brigades the U.S. has said it would begin rotating in and out of Europe.

Tensions have grown after Russian warplanes repeatedly buzzed a U.S. warship, the Donald Cook, operating in the Baltic Sea off the Russian exclave of Kaliningrad earlier this month

Mr. Work said it is an accepted practice for planes to fly over ships to announce their presence, as long as they do it from a safe altitude. But the Russian fighter planes flying over the Cook were simulating attack runs, a provocative maneuver, and came far too close, he said.

“I grew up in the Cold War in the military, and when I heard the Russians buzzed the Donald Cook I said, ‘What is new?’ But it was really new,” Mr. Work said. “This type of activity, this type of repeated simulated attack runs, at an extremely low level is unsafe and dangerous.” Russia has said the U.S. was operating too close to its military bases in Kaliningrad.

NATO and Russia have begun efforts to try to reopen military-to-military communications as well as increase transparency around exercises. Mr. Work said the U.S. and Russia effectively communicated about their separate operations in Syria.

As NATO increases its troop presence in the Baltic region, Mr. Work said, more will need to be done to avoid the potential for an accident or crisis.

One risk, Mr. Work said, is that a Russian pilot flies too close to a U.S. ship and then crashes. “You just don’t want those miscalculations and misunderstandings to occur,” he said.

Before the deployments are completed, one point of contention could be whether the infantry forces within each battalion should be from one nation or multiple. Some NATO officials believe each battalion should be from a single country, to ensure it can fight effectively.

But U.S. and NATO officials have said to make sure the force is a real deterrent to Russian aggression they would like it to operate under the alliance flag and command and control system.

Poland and the Baltic nations have been pressing for as large a presence as possible. The U.S., Germany and the U.K. have said the force must be in keeping with the 1997 NATO-Russia Founding Act, which prohibits substantial numbers of combat troops from being permanently stationed on Russia’s borders.

NATO officials said while the 1997 document doesn’t put a precise number, a force of four battalions is in keeping with those restrictions. U.S. and German officials say because the forces will rotate in and out of the Baltic region they won’t constitute a permanent force.

Russian officials have said NATO is playing games with words and is in violation of the act.

—Thomas Grove in Moscow and Nicholas Winning in London contributed to this article.