WASHINGTON (AP) — The scandal over an alleged Russian spy ring erupted at an awkward time for a White House that has staked its foreign policy record on improved cooperation with Moscow, but it appeared unlikely to do lasting damage to U.S.-Russian relations.

The administration sought to dampen tensions, while the Russian government offered the conciliatory hope Tuesday that U.S. authorities would “show proper understanding, taking into account the positive character of the current stage of development of Russian-American relations.”

The White House response was notably restrained following the dramatic announcement that 11 people assigned a decade or more to illegally infiltrate American society had been arrested. They are accused of using fake names and claims of U.S. citizenship to burrow into U.S. society and ferret out intelligence as Russian “illegals” — spies operating without diplomatic cover.

White House spokesman Robert Gibbs labored to show that the arrests were a law enforcement matter — one not driven by the president, even though President Barack Obama was informed — and played down any political consequences.

Obama was asked about the matter by reporters twice Tuesday. He declined to comment both times.

Gibbs said Obama was aware before he met with Russian President Dmitry Medvedev at the White House on Thursday that the case was under investigation, but the two leaders did not discuss it. Another White House spokesman, Tommy Vietor, said Obama did not know the exact timing of the arrests.

The FBI’s arrests of 10 Russian spy suspects had to be carried out Sunday partly because one of the defendants was scheduled to leave the United States, according to the Justice Department. But agency spokesman Dean Boyd declined to identify which of the 10 defendants arrested Sunday was planning to exit the United States.

Officials in both countries left the impression that spy rings remain a common way of doing business.

Prime Minister Vladimir Putin offered a message of restraint during a meeting at his country residence with former President Bill Clinton, who was in Moscow to speak at an investment conference.

“I understand that back home police are putting people in prison,” Putin said, drawing a laugh from Clinton. “That’s their job. I’m counting on the fact that the positive trend seen in the relationship will not be harmed by these events.”

The administration has made a high priority of improving relations with Russia. Critics say Obama has bent too far backward to accommodate the Russians, with little to show in return.

Stephen Flanagan, senior fellow at the Center for Strategic and International Studies, said some Obama critics will point to the spy scandal as evidence of a dual-track Russian approach of offering an outstretched hand while “still trying to pick your pocket” with the other.

At stake in the short term is a newly concluded nuclear arms control deal, dubbed New START, which requires a favorable vote in the U.S. Senate and approval by the Russian legislature.

More broadly, Obama wants to build the foundation for a strategic partnership with Moscow — to increase security and economic and other cooperation with the former Cold War foe.

It was that longer-term goal that the State Department emphasized in reacting to the spy case.

“We were not going to forgo the opportunity to pursue our common interests because there are things we disagreed on,” Phil Gordon, the department’s top Russia policy official, told reporters.

“I think you should see this spying issue in that context. We feel we have made significant progress in the 18 months that we have been pursuing this different relationship with Russia,” Gordon added. “We think we have something to show for it.”

By coincidence, Secretary of State Hillary Rodham Clinton is scheduled to visit the former Soviet republics of Ukraine, Georgia, Azerbaijan and Armenia in coming days, as well as Poland. Each of those countries is keenly interested in the direction of U.S.-Russian relations.

Spying has often produced pockmarks on the face of U.S.-Russian relations, even in the two decades since the collapse of the Soviet Union. The full dimensions of the latest case are yet to be made public, but the charges against the 11 suspects do not include espionage, and it was unclear what — if any — U.S. government secrets they managed to collect or transmit to Moscow.

The suspects allegedly assumed fake names and sought to obtain insights to U.S. government policymaking in ways that could benefit Russia.

Stephen Sestanovich, a Russia expert at the Council on Foreign Relations, said the matter is likely to blow over quickly, in part because the suspects are not high-value agents and appear to have accomplished little.

“The stakes for both sides are pretty small here,” Sestanovich said.

Bruce Riedel, a former CIA officer and a senior fellow at the Brookings Institution think tank, said the spy ring was “classic KGB style” in which the Russian intelligence service would plant moles and “hope that they will produce something years and maybe even decades later.”

“They’re trying to get someone into a position of influence, where someone becomes the friend of, let’s say, the president of a think tank who may become a Cabinet member in next administration,” Riedel said. “And then you have someone who not only can ask that Cabinet member questions, but might be able to influence what they’re doing.”

Leon Aron, the top Russia expert at the American Enterprise Institute, saw little chance of further diplomatic fallout in Washington or Moscow.

“I think they’ll shrug it off,” he said.

Andrew Kuchins, the top Russia expert at the Center for Strategic and International Studies, took a similar view.

“My guess is that like most spy scandals this is going to blow over,” Kuchins said.

Some analysts said they expected Moscow to consider some form of retaliation.

“There is never a good time for these things, but I am not surprised that Russian espionage continues,” said David Kramer, a former assistant secretary of state in the Bush administration and now a Russia analyst at the German Marshall Fund of the United States. “The Russians are going to respond and retaliate and that will determine what happens from here.”

Nina Khrushcheva, great-granddaugher of former Soviet leader Nikita Khrushchev and an observer of Russian political currents, said there is great suspicion about the timing of the arrests, coming shortly after Obama’s friendly meeting with Medvedev.

“The timing seemed too convenient for the conservative forces on both sides,” she said in a telephone interview from Moscow. “So there are all these conspiracies here running around: The Americans pushed it, the KGB pushed it, the reset will go to hell.”

She was referring to the Obama administration’s efforts to “reset” relations with Russia after a period of tensions, particularly following Russia’s armed invasion of Georgia in August 2008.

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Associated Press writers Matthew Lee, Desmond Butler, Lolita C. Baldor and Doug Birch and Ben Feller contributed to this report.