The United States has badly underestimated the level of anger in Germany over its spying operations and the damage could be long-lasting if Washington fails to back off, former US officials said on Wednesday.

Germany's dramatic decision last week to throw out the CIA station chief in Berlin took the Americans by surprise and conveyed a deep frustration with Washington, which has mounted for months since revelations of US eavesdropping on Chancellor Angela Merkel's mobile phone.

"It's unprecedented. And it's an unmistakable signal about unhappiness in the German government," said James Lewis, a former US intelligence official.

The shock move to expel the most senior US intelligence officer in Berlin came after authorities caught the Americans running two alleged double agents employed in government offices, a revelation that represented the last straw for Berlin.

The Germans have a valid complaint to say "this is too much, you've gone too far, you need to back off," said Lewis, a senior fellow at the Center for Strategic and International Studies.

The alleged spying raised questions about whether the White House was keeping a close eye on what its intelligence agencies were up to inside an allied country, and whether it was worth the political cost, experts said.

In one instance, the US allegedly paid money to a low-level agent in the BND foreign intelligence service to pass documents from a parliamentary committee's probe into ex-intelligence contractor Edward Snowden's allegations of snooping in Germany.

To jeopardize ties with Germany for information that could be obtained without spying suggested a bureaucracy on autopilot, a former Western diplomat said.

"It's stupidity beyond belief," the ex-diplomat said.

President Barack Obama's deputies needed to be reviewing any espionage in Germany with "a very high level of scrutiny," said Kori Schake, who worked on the National Security Council under former president George W.Bush.

"People need to be making a very careful risk analysis. And I think at least the German government doesn't believe we are," said Schake, a fellow at Stanford University's Hoover Institution.

Germany has long resented being excluded from the so-called "Five Eyes" arrangement involving intelligence agencies from Australia, Britain, Canada, New Zealand and the US.