The media groups argued that by expanding the definition of "critical infrastructure information," the cybersecurity bill would exempt more records from public disclosure.
Senate Majority Leader Harry Reid (D-Nev.) plans to bring the legislation straight to the Senate floor without any committee markups.
The bill's backers note that Congress has been considering cybersecurity legislation for several years and that the bill incorporates elements from other measures that have already been through the committee process.
"We urge you to not fast track this bill," the groups wrote. "The unaddressed issues we have identified demand a more careful and thorough consideration."
A spokeswoman for the Homeland Security and Government Affairs Committee said the the bill's sponsors plan to work with the media groups and other critics of the legislation before the bill comes to a vote in the Senate.
"We understand that there's a need to balance transparency and make sure that our critical infrastructure information is secure," she said. "We will continue to work with groups and experts to strike the right balance."