WASHINGTON — A presidential advisory committee charged with examining the operations of the National Security Agency has concluded that a program to collect data on every phone call made in the United States should continue, though under broad new restraints that would be intended to increase privacy protections, according to officials with knowledge of the report’s contents.

The committee’s report, the officials said, also argues in favor of codifying and publicly announcing the steps the United States will take to protect the privacy of foreign citizens whose telephone records, Internet communications or movements are collected by the N.S.A. But it is unclear how far that effort would go, and intelligence officials have argued strenuously that they should be under few restrictions when tapping the communications of non-Americans abroad, who do not have constitutional protections under the Fourth Amendment.

The advisory group is also expected to recommend that senior White House officials, including the president, directly review the list of foreign leaders whose communications are routinely monitored by the N.S.A. President Obama recently apologized to Chancellor Angela Merkel of Germany for the N.S.A.’s monitoring of her calls over the past decade, promising that the actions had been halted and would not resume. But he refused to make the same promise to the leaders of Mexico and Brazil.

Administration officials say the White House has already taken over supervision of that program. “We’re not leaving it to Jim Clapper anymore,” said one official, referring to the director of national intelligence, who appears to have been the highest official to review the programs regularly.