But while American officials remained angry at China for letting Mr. Snowden fly to Moscow, they and their Russian counterparts toned down the red-hot language that threatened a deeper rupture in relations. Mr. Putin said he saw little to gain in the conflict. “It’s like shearing a piglet,” he said. “There’s a lot of squealing and very little wool.” Some American officials interpreted the comment as a positive signal and speculated that Mr. Snowden would be sent to another country that could turn him over.

Yet the Russian president’s remarks during an official visit to Finland also underscored what may be the lasting damage the case has caused for American relations with both Moscow and Beijing. In noting that Mr. Snowden viewed himself as a “human rights activist” who “struggles for freedom of information,” Mr. Putin made clear that it would be harder for President Obama to claim the moral high ground when he presses foreign leaders to stop repressing dissenters and halt cyberattacks…

The Obama administration was relying on Deputy Secretary of State William J. Burns, a low-key, respected former ambassador to Russia, to negotiate with Moscow. The administration argued Tuesday that even though the United States and Russia did not have an extradition treaty, Washington had regularly sent back Russians sought by Moscow. Over the last five years, the Department of Homeland Security said Tuesday, the United States had returned 1,700 Russian citizens, with more than 500 of them being “criminal deportations.”

But in Moscow, Mr. Snowden was being compared to cold war dissidents. “I have never heard of any case when the United States would extradite someone’s fugitive spy,” said Vlacheslav Nikonov, a member of Parliament. “It just never happened. Why would they expect that would happen?”