Public Knowledge, the Electronic Frontier Foundation, Reddit and Boing Boing were among the groups that signed the letter.
The Library of Congress based its decision on the Digital Millennium Copyright Act (DMCA), which bans people from circumventing a "technological measure" to access a copyrighted work.
Legislation from Senate Judiciary Committee Chairman Patrick LeahyPatrick LeahySenate confirms first nominees of Trump era Senate gears up for battle over Trump's CIA pick Overnight Tech: Meet the key players for Trump on tech | Patent chief staying on | Kerry aide goes to Snapchat | Uber's M settlement MORE (D-Vt.) would overturn the Library of Congress's decision and order the agency to consider expanding the exemption to cover tablets.
But the groups argued that the only permanent fix would be to amend the DMCA. They claimed that provisions of the act interfere with "consumer rights and competition policy" in areas beyond unlocking mobile devices.
"Congress must take action to ensure that laws and policies are keeping up with the pace of technological change," they wrote. "Not addressing these questions will stunt advances in access to digital media for people with disabilities and may prevent new innovations and competitive uses for emerging devices, as uncertainties around the law and the three-year cycle creates a chilling effect for individuals, businesses, innovators and investors who may be covered by the law."