The National Security Agency (NSA) is reportedly ending the practice of collecting American emails and text messages that mention the name of a foreigner who is under U.S. surveillance.

Officials familiar with the matter told The New York Times on Friday that the NSA made the change after it ended up collecting bundled messages, which included domestic communications.

According to the Times, some internet companies transmitted multiple messages as a unit, meaning that if one message within the group contained an email address of a foreign target, the entire bundle would automatically be surveilled.

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The practice has been a subject of heated debate between national security officials and privacy advocates, who argued that the warrantless collection of private data is not constitutional.

Officials who supported the practice, however, maintained that the surveillance program is key when it comes to identifying people who may have links to terrorism.

Civil liberties advocates called the move a "partial fix" while urging Congress to reform a key portion of the Foreign Intelligence Surveillance Act (FISA) that allows for the collection of intelligence on foreign targets outside the U.S. without a warrant.

“This development underscores the need for Congress to significantly reform Section 702 of FISA, which will continue to allow warrantless surveillance of Americans," Neema Singh Guliani, American Civil Liberties Union legislative counsel, said in a statement.

"While the NSA’s policy change will curb some of the most egregious abuses under the statute, it is at best a partial fix. Congress should take steps to ensure such practices are never resurrected and end policies that permit broad, warrantless surveillance under Section 702, which is up for reauthorization at the end of the year,” Guliani added.