Four Democratic senators have sent a letter to the director of national intelligence expressing concerns about the scope of the collection of Americans’ e-mails and phone calls under a National Security Agency program that targets foreigners overseas.

The lawmakers, led by Jon Tester (D-Mont.), told Director of National Intelligence James R. Clapper Jr. that they were concerned by recent reports by The Washington Post and an independent executive branch panel about the surveillance.

The Post examined 160,000 communications intercepted under the program, which was authorized by Section 702 of the Foreign Intelligence Surveillance Act as amended in 2008. The law does not require individualized warrants.

The Post found that “nearly half of the surveillance files . . . contained names, e-mail addresses or other details that the NSA marked as belonging to U.S. citizens or residents.”

“This revelation raises significant doubts about whether we are striking the right balance between securing our nation and upholding the privacy and civil liberties of our citizens,” the senators wrote in the letter, which was dated Thursday.

The independent panel, known as the Privacy and Civil Liberties Oversight Board, found that Section 702 surveillance is legal and has made “a substantial contribution” to U.S. efforts to prevent terrorist acts. It also found no indication of abuse.

But the board also said that certain aspects of the program push it “close to the line” of being unconstitutional. Such aspects, it said, include “the unknown and potentially large scope of the incidental collection of U.S. persons’ communications.”

The board also noted that the program’s rules “potentially allow a great deal of private information about U.S. persons to be acquired by the government.”

Tester and his colleagues wrote that while incidental collection of Americans’ data “may be unavoidable at the time of collection, we remain concerned that this personal data is being obtained and queried without a warrant, and stored for an unknown and possibly indefinite period of time.”

Intelligence officials have noted that a federal court in Oregon recently upheld the program’s constitutionality. They say that the program is subject to multiple layers of oversight, including from Congress, a surveillance court, the Justice Department, the Office of the Director of National Intelligence and the NSA inspector general.

“We’re not just randomly looking to collect communications of U.S. persons or non-U.S. persons,” Robert S. Litt , general counsel for the ODNI, said at a security forum in Aspen, Colo., this week. “It all has to be driven by valid foreign intelligence needs.”

The senators urged Clapper to erase all Americans’ communications records that have been collected “incidentally” and that contain no foreign intelligence. They asked him to provide answers to a series of questions about incidental collection and other aspects of Section 702. President Obama’s review board on surveillance policy, a separate group from the privacy board, made the same recommendation in December.

The senators sought information on how many Americans have had their information collected under Section 702.

In a recent blog post, the privacy board’s chairman, David Medine, said the panel investigated this question and confirmed “that the government does not know the answer.”

It is difficult to determine whether even a single e-mail address is used by a U.S. person, and to do so in a way that does not invade people’s privacy, he said.

The Post said in its story: “It is not obvious why the NSA could not offer at least a partial count given that its analysts routinely pick out ‘U.S. persons’ and mask their identities, in most cases, before distributing intelligence reports.”

The other three senators were Mark Begich (Alaska), Jeff Merkley (Ore.) and John Walsh (Mont.)