To some extent, Russia is the familiar threat at this meeting. Its aggression toward Ukraine dominated the last NATO summit meeting in Wales, and two years later, the alliance has put in place military measures to deter it. NATO is strengthening its eastern flank by deploying four rotational battalions, one led by the United States, in Estonia, Latvia, Lithuania and Poland.

The alliance is expected to declare that the initial phase of its missile-defense system is finally operational. And the leaders are scheduled to discuss ways to deter members from cyberattacks, having elevated cyberwarfare to the same status as air, land and naval warfare.

Over dinner on Friday night, the leaders will discuss how best to deal with President Vladimir V. Putin of Russia. Mr. Obama will be able to deliver a briefing, having spoken with Mr. Putin the day before he left Washington. Officials suggested the conversation was starchy, with the president scolding Mr. Putin for a “significant uptick in fighting in Eastern Ukraine” and urging him to press the Syrian government to abide by a partial cease-fire.

Mr. Rhodes disputed a report from the Kremlin that the two countries were moving toward military cooperation in Syria. “If the trends of the last several weeks continue,” he said, referring to recent Russian behavior regarding Syria, “they’ve been moving in the wrong direction.”

Administration officials said Mr. Obama would emphasize ways NATO could cooperate militarily with the European Union — modest but symbolically significant gestures to counter the rifts exposed by the British vote. Those include joint military exercises, coordinating cyberdefense strategy and joint patrols of the central Mediterranean Sea.

On Afghanistan, too, there is scope for unity. Mr. Obama, who on Wednesday described the security situation in the country as “precarious,” announced that the United States would again delay its drawdown of troops, leaving 8,400 soldiers there until the end of his presidency. That commitment, analysts said, would make it easier for other NATO members to deploy troops.