The Senate Intelligence Committee, whose chairman, Dianne Feinstein (D-Calif.), has defended the surveillance efforts, asked the NSA on Tuesday to publicly explain programs that use telephone and Internet records “so that we can talk about them, because I think they’re really helpful,” she said.

Calls for greater transparency, rather than new limits on government powers, have been the main public fallout in the days since The Washington Post and Britain’s Guardian newspaper reported that the NSA was collecting and analyzing data flowing through nine U.S. Internet companies. The program, called PRISM, reportedly was focused on foreigners but also collected data on U.S. citizens and residents that could, under certain conditions, be reviewed by officials.

Both Google and Facebook, whose business models depend on hundreds of millions of users voluntarily sharing information about themselves, have denied participating in a surveillance program as broad as described in news reports on PRISM. Yet all the companies named in reports have struggled to stanch the damage to their reputations as stewards of personal privacy.

Google on Tuesday published an open letter to Attorney General Eric H. Holder Jr. and FBI Director Robert S. Mueller III requesting the right to report publicly the numbers and scope of national security data requests, a move that would allow Google to significantly expand its semiannual “transparency reports” on the information sought by courts and police worldwide.

“Google has nothing to hide,” wrote Chief Legal Officer David Drummond. The Justice Department declined to comment.

Facebook soon after issued a statement suggesting that it may start publishing its own “transparency reports” — a move the company has long resisted. “We urge the United States government to help make that possible by allowing companies to include information about the size and scope of national security requests we receive, and look forward to publishing a report that includes that information,” wrote Ted Ullyot, general counsel to Facebook. (Washington Post Co. Chairman Donald E. Graham is on Facebook’s board.)

Microsoft issued a statement as well, saying that greater transparency “would help the community understand and debate these important issues.”

Yahoo said late Tuesday that “we recognize the importance of privacy and security, and we also believe that transparency . . . will help build public trust.”

Google, Facebook and Yahoo are particularly vulnerable to public fallout because they make money mainly from advertising and can charge significantly higher rates when they have enough personal information to target an ad message precisely to a user’s individual interests. Apple and Microsoft, by contrast, profit mainly from selling products.

“The NSA doesn’t care about its brand,” said Chris Soghoian, an American Civil Liberties Union technologist who has worked for tech companies and the Federal Trade Commission. “It’s the Internet companies whose brands are suffering.”

One major company not mentioned as a participant in PRISM was the popular social-media platform Twitter. Although the company hasn’t commented directly on PRISM, many in the technology community believe it may have resisted NSA requests to participate. The company is ranked by the Electronic Frontier Foundation, a privacy group, as the most protective of user information among major Internet companies.

In 2011, the firm told Justice Department officials that it would not hand over information about users related to a government investigation of WikiLeaks without a court order. Last year, it appealed an order by a U.S. District Court judge in New York to hand over records of a Twitter user associated with the Occupy Wall Street movement.

On Tuesday, the company’s general counsel, Alex Macgillivray, tweeted a message of support for efforts to require greater government transparency on data collection, including the orders, called national security letters, that can require companies to turn over extensive information while sharply limiting any disclosure about the request. “We’d like more NSL transparency and @Twitter supports efforts to make that happen.”

The most valuable information about Twitter users is their Internet addresses, which would allow authorities to track the location and habits of users. E-mails and documents are of greater interest to intelligence officials, said Peter Eckersley, technology project director for the Electronic Frontier Foundation.

“If these companies can’t be transparent with users about their participation in surveillance with the U.S. government, they will lose a lot of business,” he said. “If foreign companies know that using Google Docs or e-mail will expose them to U.S. spies, they will choose a different platform.”

The reaction to revelations about the NSA program has been particularly strong in Europe, where officials are developing a new data privacy law that has been the subject of lobbying by U.S. officials concerned that strict new rules could hinder the reach of American tech companies on the continent.

Tech giants such as Google, Apple and Facebook have been among the few bright spots in the U.S. economy as it slogged through the recent downturn, and most are counting on overseas business to continue fueling their growth.

News that the NSA was using major U.S. companies to monitor foreign Internet users has complicated their positions abroad, according to a letter sent to Holder on Monday by European Commission Vice President Viviane Reding. It warned that PRISM threatened to “undermine the trust” of Europeans. She requested answers to a series of questions about the program by Friday.

Ed O’Keefe, Greg Miller and Peter Finn in Washington and Michael Birnbaum in Berlin contributed to this report.