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“It won’t prevent further escalation between Russia and Ukraine — only Putin’s separate decisions can achieve that outcome,” Mr. O’Hanlon said. “But it will help prevent inadvertence or accident or a local commander operating on his own from stoking or causing a crisis that top leadership in Washington and Moscow have no desire for.”

U.S.-Russia efforts to improve communication come during an auspicious time, when Russian forces and NATO allies are flexing their military muscles near Russia’s border with Ukraine.

Ongoing dialogue between the military leaders is important because that is what keeps destabilizing incidents at bay, Col. Thomas said.

Gen. Dempsey believes that being able to have transparent and candid conversations with his counterpart is vitally important,” he said.

Defense Secretary Chuck Hagel has also maintained an ongoing conversation with his Russian counterpart.

Mr. Hagel repeatedly called for a de-escalation of the situation between Russia and Ukraine and recently reiterated that message when talking to Russian Defense Minister Sergei Shoigu on Monday, Pentagon spokesman Rear Adm. John Kirby said.

After that conversation, Pentagon officials issued a statement that implied Mr. Hagel had the upper hand during his dialogue with Mr. Shoigu. Mr. Hagel, the statement said, sought clarification on Russia’s intentions toward eastern Ukraine and called for an end to Russia’s “continued aggression.”

Russian media, however, has portrayed the conversation as somewhat contentious. During the discussion, Mr. Shoigu asked Mr. Hagel to “turn down the rhetoric” over the Ukraine crisis, according to the Moscow Times.

Adm. Kirby told reporters Tuesday that the dialogue between the officials remained civil, even though it was occasionally “terse.” Both men, he said, agreed to continue discussing the crisis.

• This article is based in part on wire service reports