Senator Rand Paul, Republican of Kentucky, said he was skeptical that any changes passed by Congress would go far enough. “It gives me optimism that it won’t be completely brushed under the rug,” he said. “However, I’ve been here long enough to know that in all likelihood when there’s a problem, you get window dressing.”

The FISA court, which oversees national security surveillance inside the United States, has been criticized because it hears arguments only from the Justice Department without adversarial lawyers to raise opposing views, and because Chief Justice John G. Roberts Jr. has unilateral power to select its members. Echoing proposals already floated in congressional hearings and elsewhere, the advisory group backs the view that there should be a “public interest advocate to represent the interests of privacy and civil liberties” in classified arguments before the court. It also says the power to select judges for the surveillance court should be distributed among all the Supreme Court justices.

In backing a restructuring of the N.S.A.’s program that is systematically collecting and storing logs of all Americans’ phone calls, the advisers went further than some of the agency’s backers in Congress, who would make only cosmetic changes to it, but stopped short of calling for the program to be shut down, as its critics have urged. The N.S.A. uses the telephone data to search for links between people in an effort to identify hidden associates of terrorism suspects, but the report says it “was not essential to preventing attacks.”

Currently, the government obtains orders from the surveillance court every 90 days that require all the phone companies to give their customers’ data to the N.S.A., which commingles the records from every company and stores it for five years. A small group of analysts may query the database — examining records of everyone who is linked by up to three degrees of separation from a suspect — if the analyst has “reasonable, articulable suspicion” that the original person being examined is linked to terrorism.

Under the new system proposed by the review group, such records would stay in private hands — either scattered among the phone companies or pooled into some kind of private consortium. The N.S.A. would need to make the case to the surveillance court that it has met the standard of suspicion — and get a judge’s order — every time it wanted to perform such “link analysis.”