The bill is a revised version of a law passed by the House in May 2014 before being voted down by the Senate.
The proposed legislation is set to reauthorize the controversial Section 215 of the USA Patriot Act until 2019 but will add restrictions to the provision set to expire June 1.
Last week, Senate Majority Leader Mitch McConnell unveiled legislation to extend the Patriot Act without making any changes.
The Patriot Act was signed into law by former US President George Bush in October 2001, just over a month after the September 11 attacks, to allow mass surveillance in a bid to deter and punish terrorist acts in the United States and abroad.
Under the proposed Freedom Act the NSA will have to secure a court order before obtaining records from private phone companies.
"It enhances civil liberties protections, increases transparency for both American businesses and the government, ends the bulk collection of data, and provides national security officials targeted tools to keep America safe from foreign enemies," House lawmakers behind the bill said, in a joint statement quoted by local media.
"The disclosures of the last two years make clear that we need wholesale reform. Congress should let Section 215 sunset as it's scheduled to, and then it should turn to reforming the other surveillance authorities that have been used to justify bulk collection," Jameel Jaffer, the American Civil Liberties Union deputy legal director, said.
The House judiciary committee plans to vote on the bill Thursday before passing it on to Congress, which will have a month to decide on the use of US surveillance programs in the future.