The bill still needs to be passed by the US Senate before heading to President Donald Trump for his signature.
Both House of Representatives Speaker Paul Ryan and Minority Leader Nancy Pelosi spoke against the measure, which drew opposition and support from both Republicans and Democrats.
During the debate, Ryan warned that the amendment, if approved, would create a firewall between intelligence on terrorist plots hatched overseas and law enforcement in the United States.
"You pass the Amash Amendment and defeat this underlying bill, we go back to those days when we are flying blind on protecting our country from terrorism," Ryan stated.
The bill will extend the existing surveillance programs for foreigners for six years with minor changes. At the same time, the House will consider an amendment that suggests banning the National Security Agency (NSA), the Federal Bureau of Investigation (FBI) and other special services from reading US nationals' messages, which may find themselves in extensive intelligence databases "incidentally" collected across the world.
Mass surveillance by US authorities in the United States and other countries was revealed in classified US documents published by former NSA employee turned whistleblower Edward Snowden in 2013, prompting criticism from governments, as well as human right advocates and activist groups across the globe. Russia granted the whistleblower a temporary asylum after he fled the United States.