U.S. Secretary of State John Kerry landed in Rome and Paris to talk about Mideast peace, Syria and Iran but was confronted by outrage over the sweep and scope of U.S. snooping abroad.

President Barack Obama already has defended America's surveillance dragnet to leaders of Russia, Mexico, Brazil, France and Germany and was even quizzed about it during his birthday appearance on late-night television.

In the short run, Obama and Kerry are trying to quell international anger over classified disclosures by former National Security Agency contractor Edward Snowden. Longer term, Snowden's revelations about NSA tactics — that allegedly include tapping up to 35 world leaders' cellphones — threaten to undermine U.S. foreign policy in a host of areas.

It's the vacuum-cleaner approach to data collection that has rattled foreign allies.

"The magnitude of the eavesdropping is what shocked us," former French Foreign Minister Bernard Kouchner said in a radio interview. "Let's be honest, we eavesdrop too. Everyone is listening to everyone else. But we don't have the same means as the United States, which makes us jealous."

Meanwhile, thousands of people marched on the National Mall in Washington, D.C. on Saturday to protest against the NSA's surveillance program.

Organizers of the rally, the Stop Watching Us Coalition, want to end government spying on American citizens.

Where in the world isn't the NSA?

The disclosures not only raise the question: Where in the world isn't the NSA? They also sparked debate about whether tapping the phones of allies is a step too far. The question might already be moot. The British ambassador to Lebanon, Tom Fletcher, tweeted this week: "I work on assumption that 6+ countries tap my phone. Increasingly rare that diplomats say anything sensitive on calls."

Diplomatic relations are built on trust. If America's credibility is in question, the U.S. will find it harder to maintain alliances, influence world opinion and maybe even seal trade deals.

The magnitude of the eavesdropping is what shocked us. - French Foreign Minister Bernard Kouchner

Spying among allies is not new. Madeleine Albright, secretary of state during the Clinton administration, recalled being at the United Nations and having the French ambassador ask her why she said something in a private conversation that the French had apparently intercepted. The French government protested revelations this week that the NSA had collected 70.3 million French-based telephone and electronic message records in a 30-day period.

Albright says Snowden's disclosures have been very damaging to U.S. policymakers.

"A lot of the things that have come out, I think are specifically damaging, because they are negotiating positions and a variety of ways that we have to go about business," Albright said at a conference hosted by the Center for American Progress in Washington. "I think it has made life very difficult for Secretary Kerry. ... There has to be a set of private talks that, in fact, precede negotiations and I think it makes it very, very hard."

Free trade talks

The spy flap could give the Europeans leverage in talks with the U.S. on a free trade agreement, which would join together nearly half of the global economy. "If we go to the negotiations and we have the feeling those people with whom we negotiate know everything that we want to deal with in advance, how can we trust each other?" Martin Schulz, president of the European Parliament, asked.

Claude Moniquet, a former French counterintelligence officer and now director of Brussels-based European Strategic Intelligence and Security Center, said the latest NSA flap came at a good time for Europe "to have a lever, a means of pressure ... in these negotiations."

To Henry Farrell and Martha Finnemore at George Washington University, damage from the NSA disclosures could "undermine Washington's ability to act hypocritically and get away with it."

The danger in the disclosures "lies not in the new information that they reveal but in the documented confirmation they provide of what the United States is actually doing and why," they wrote in Foreign Affairs. "When these deeds turn out to clash with the government's public rhetoric, as they so often do, it becomes harder for U.S. allies to overlook Washington's covert behaviour and easier for U.S. adversaries to justify their own."

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 sweeping nature of NSA surveillance goes against the Obama administration's claim that much of U.S. espionage is carried out to combat terrorism, she says.

"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."

Push for end to eavesdropping

The Obama administration's rebuttal to outrage has been that the U.S. is gathering foreign 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. "He certainly recognizes that as we look to pursue a range of diplomatic priorities, whether that's working together on global issues like Syria or Iran or TTIP (the Transatlantic Trade and Investment Partnership), it would really be a mistake to let these disclosures get in the way," she said.

Most governments have not retaliated, but some countries are pushing back.

Germany and France are demanding that the Obama 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 cancelled 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 United Nations General Assembly resolution that would guarantee people's privacy in electronic communications.

A European Parliament committee in Brussels approved sweeping data protection 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 terror-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."