The NATO moves announced Thursday were mostly symbolic, although Russia quickly reacted to the British announcement. Dmitri S. Peskov, a spokesman for Mr. Putin, told journalists that any increased presence of British troops in Eastern Europe would be regrettable, according to Agence France-Presse, adding that it would amount to Britain’s using an alleged Russian threat as camouflage to press ahead with NATO expansion. Russia, he said, would respond with “parity.”

As Western defense ministers — including the United States defense secretary, Ashton B. Carter — met here on Thursday, much of the discussion focused on Russia and Syria, and in particular the timing of the launch of 26 cruise missiles across more than 900 miles, from the Caspian Sea, into Syria.

“They did this the day before a meeting of NATO defense ministers,” one NATO official said, speaking on the condition of anonymity because of the delicate nature of the negotiations. “Obviously, that is a message, but who can say what Putin is thinking.”

But even as the alliance sought to project its power toward the Russian border, and to remind Moscow that Russian maneuvers in Turkish airspace could invite a response, several NATO officials expressed frustration that they did not see a clear path out of the increasingly complicated tangle that has become NATO’s relationship with Russia. One said that the expansion of NATO toward Russia’s borders was the reason Mr. Putin was now maneuvering for elbow room, both in Eastern Europe and in trying to retain his access to the Mediterranean Sea through Syria.

Mr. Putin insists that Russia’s intervention in Syria and its support for a ground offensive there — which appeared to be an effort involving Iran, the Lebanese militia Hezbollah and the pro-government army, which is loyal to Syria’s embattled president, Bashar al-Assad — is intended to target militants from the Islamic State. But Western officials say he is using that pretext to batter other insurgent groups that have been trying to overthrow Mr. Assad.

“The Russians are not mainly targeting ISIS, but they are targeting other opposition groups and they are supporting the regime,” Mr. Stoltenberg said. “And I call on Russia to play a constructive and cooperative role in the fight against ISIS, not to continue to support the Assad regime. Because to support the regime is not a constructive contribution to a peaceful and lasting political solution in Syria.”