They claim the disclosures forced Washington to abandon its "naming-and-shaming campaign against Chinese hacking."
The revelations could undercut Washington's effort to fight terrorism, says Kiron Skinner, director of the Center for International Relations and Politics at Carnegie Mellon University. The broad nature of NSA surveillance goes against the Obama administration's claim that much of U.S. espionage is carried out to combat terrorism, she said.
"If Washington undermines its own leadership or that of its allies, the collective ability of the West to combat terrorism will be compromised," Skinner said. "Allied leaders will have no incentive to put their own militaries at risk if they cannot trust U.S. leadership."
The administration asserts that the U.S. is amassing intelligence of the type gathered by all nations and that it's necessary to protect the U.S. and its allies against security threats.
Kerry discussed the NSA affair in Europe with French and Italian officials this past week.
Most governments have not retaliated, but some countries are pushing back.
Germany and France are demanding that the administration agree by year's end to new rules that could mean an end to reported American eavesdropping on foreign leaders, companies and innocent citizens.
Brazilian President Dilma Rousseff canceled her official state visit to the White House. She ordered measures aimed at greater Brazilian online independence and security after learning that the NSA intercepted her communications, hacked into the state-owned Petrobras oil company's network and spied on Brazilians.
Brazil says it is working with other countries to draft a U.N. General Assembly resolution that would guarantee people's privacy in electronic communications.
A European Parliament committee approved rules that would strengthen online privacy and outlaw the kind of data transfers the U.S. is using for its spying program.
European lawmakers have called for the suspension of an agreement that grants U.S. authorities access to bank data needed for terrorism-related investigations.
"We need trust among allies and partners," said German Chancellor Angela Merkel, whose cellphone was allegedly tapped by the NSA. "Such trust now has to be built anew."