WASHINGTON — They doffed their jackets and bonded over burgers, talking about everything from trade and geopolitics to their families. Everything, that is, except the spies that the government of one had hidden in a house just a few miles away and that the government of the other was about to arrest.

The roundup of a suspected Russian spy ring did more than disrupt a years-old deep-cover operation inside the United States — it cast a shadow over President Obama’s effort to transform the relationship between the two countries. The timing of the arrests, coming barely 72 hours after President Dmitri A. Medvedev’s White House visit, frustrated Mr. Obama’s team. But as prosecutors assemble their case, Mr. Obama has resolved not to let the ghosts of the 20th century get in the way of his goals in the 21st.

Mr. Obama’s administration said Wednesday that it would not expel Russian diplomats and it expressed no indignation that its putative partner was spying on it. Mr. Obama’s plan is to largely ignore the issue publicly, leaving it to diplomats and investigators to handle, while he moves on to what he sees as more important matters.

“We would like to get to the point where there is just so much trust and cooperation between the United States and Russia that nobody would think of turning to intelligence means to find out things that they couldn’t find out in other channels,” Philip Gordon, the assistant secretary of state in charge of Russia, told reporters. “We’re apparently not there yet. I don’t think anyone in this room is shocked to have discovered that.”

But the spy scandal could embolden critics who argue that Mr. Obama has been overly optimistic about his capacity to reset a relationship freighted by longstanding suspicion and clashing interests. The episode could complicate Mr. Obama’s efforts to persuade the Senate to approve the new arms control treaty he negotiated with Mr. Medvedev.

“It ought to reset our rosy view of Russia and remind us that Russia is not a trustworthy ally,” Senator Christopher S. Bond of Missouri, the ranking Republican on the Senate intelligence committee, said in an interview. Harking back to Ronald Reagan’s approach, Mr. Bond said: “We have to deal with them. But wasn’t there a great president who said, ‘Trust but verify’?”

Even if Mr. Obama can assuage doubts on the treaty, the scandal has underscored the limits of the new relationship.

“The spy scandal is unlikely to derail the reset because both sides have too much invested in the success of the current agenda,” said Angela E. Stent, a former National Intelligence Council official now at Georgetown University. “But it is a cautionary reminder that the U.S.-Russian relationship remains a selective partnership where cold war legacies persist.”

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