Brazilian President Dilma Rousseff canceled a state visit to the White House over the issue. She criticized the U.S. in a speech before the United Nations General Assembly.

"The safety of a citizen of one country should not be guaranteed by the violation of human and civil rights which are fundamental to citizens of another country," said Rousseff.

But General Alexander says many Americans who oppose the NSA's collection of phone and email records are being misled by inaccurate reports in the media.

At the cybersecurity seminar, he said the NSA is not collecting content from the phone calls or emails it monitors.

He also said U.S. allies appreciate the data gathering because it also protects their countries from terror attacks.

"Many people have asked me, how has this impacted your relationship with allies? Here is what I get: 'Keep working with us," he said. "The intelligence you get us to defend our country is what we really need.'"

The Senate committee's chairman, Democratic Senator Dianne Feinstein, says the NSA should continue gathering phone and email records. She favors a less restrictive bill that would bar the NSA from collecting the content of phone calls and email messages.