"We believe the program is legal. I am hopeful it's sustained by the president, maybe in slightly different form," said Democratic Sen. Dianne Feinstein, chairwoman of the Senate Intelligence Committee and an important voice in the NSA debate.
Snowden leaked secrets about mass collection of telephone data and other secret eavesdropping programs to newspapers before fleeing to Hong Kong and then to Moscow. Journalists with access to Snowden's materials say there are many more disclosures to come.
When the Snowden disclosures first appeared last June, Obama said, "We've struck the right balance" between the desire for information and the need to respect Americans' privacy.
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But after a disclosure of U.S.eavesdropping on German Chancellor Angela Merkel's mobile phone, he called for "additional constraints" on American surveillance practices.
Privacy advocates have been appealing for greater protections for Americans' constitutional right to privacy. Some privacy advocates will doubtless be pleased by Obama's plan but other NSA critics may say the president did not go far enough.
"While we welcome the president's acknowledgement that reforms must be made, we warn the president not to expect thunderous applause for cosmetic reforms. We demand more than the illusion of reform," said David Segal, executive director of Demand Progress, a civil liberties advocacy organization.
As well as the tension with Germany, the eavesdropping has disrupted relations with some other nations. Brazilian President Dilma Rousseff postponed a state visit to the United States to express her anger over U.S. intrusions in her country.