An undated handout photograph made available by the National Security Agency shows the agency’s headquarters in Fort Meade, Md. (National Security Agency/Via European Pressphoto Agency)

An independent executive-branch board has concluded that a major National Security Agency surveillance program targeting foreigners overseas is lawful and effective but that certain elements push “close to the line” of being unconstitutional.

The “unknown and potentially large” collection by the agency of e-mails and phone calls of Americans who communicate with foreign targets is one aspect that raises concerns, the Privacy and Civil Liberties Oversight Board said in a report released online Tuesday night.

But the board did not go as far in its recommendations as privacy advocates would like. For instance, it would leave in place the government’s ability to conduct warrantless searches for Americans’ communications in the data gathered by the NSA.

At issue is a program authorized by Section 702 of the FISA Amendments Act of 2008, which was an effort to bring under the law a surveillance effort begun after the 2001 terrorist attacks and run exclusively by the executive branch.

Under the law, the government can target “non-U.S. persons reasonably believed to be located abroad.” However, it is not required to obtain individualized warrants, even though the collection is done inside the United States.

The 191-page report comes after a year of heightened debate and scrutiny over U.S. surveillance practices in the wake of leaks of NSA documents to journalists by former agency contractor Edward Snowden.

In January, the board issued a strongly worded report that concluded that a different NSA program involving the collection of Americans’ phone call records was illegal and should end. The agency’s gathering of billions of such “metadata” records — numbers dialed, times and durations — did not comply with the law, the board found.

Unlike the phone metadata program, Section 702 “fits within the ‘totality of the circumstances’ standard of reasonableness under the Fourth Amendment,” the board said.

It also has enabled the government to obtain a greater range of foreign intelligence than it otherwise would be able to, and to do so quickly and effectively, the board said.

The board also said the program has led the government to identify previously unknown individuals involved in international terrorism.

But certain features raise privacy concerns, the board said. For instance, though the law does not explicitly permit it, the agency collects communications in which a target’s e-mail address or phone number is mentioned — even if it is in the body of an e-mail as opposed to the “to” or “from” line.

As a result of this practice, known as “about” collection, both parties to the communication could be U.S. persons or inside the United States. This is largely due to technical difficulties with determining the location of the parties at the time of collection, the board said.

Also of concern is the use of queries to search for the communications of specific U.S. persons within the database of information already gathered. Sometimes called “backdoor searches,” the practice was the target of a House vote last month to bar such searches.

The board was divided on the issue. Two members recommended court approval — but with less than a warrant based on probable cause. Two members said sign-off by an executive-branch agency was sufficient. And a fifth declined to weigh in.

“The board’s recommendations are surprisingly anemic, particularly in light of its much more robust approach in its January report on the bulk collection of Americans’ telephone records,” said Elizabeth Goitein, co-director of the Brennan Center for Justice’s Liberty and National Security Program.

The board also recommended, among other things, that the NSA’s targeting procedures be revised to specify criteria for determining the expected foreign intelligence value of a particular target. And it urged that the NSA annually count the number of phone calls acquired in which one caller is located in the United States, the number of e-mails that originate or terminate in the United States and the number of queries performed for U.S. persons’ data.