The groups filed a motion late Wednesday saying unsealing the documents would allow the public to oversee the actions of its judicial and executive branches of state government.
The investigation started in August 2012 and focuses on alleged illegal campaign fundraising, spending and coordination by conservative groups, the governor's campaign and others.
Theodore Boutrous, attorney for the media groups, said keeping the documents secret violates the First Amendment rights of the press and public.
"It is undisputed that the public has a First Amendment right of access to 'any documents' upon which the Court may rely 'in making its decisions,'" Boutrous wrote in a brief filed with U.S. District Judge Rudolph Randa.
Attorneys for Milwaukee County District Attorney John Chisholm agree all the documents should be unsealed. Prosecutor Dean Nickel said in a brief that the investigation had already become so widely publicized that unsealing the documents wouldn't hinder the investigation, known as a John Doe.
Attorneys for the Wisconsin Club for Growth, which is under investigation, want to keep hundreds of pages secret. Two other anonymous groups have asked that all documents from the investigation remain under seal because they say making the documents public would reveal private information about them or their political opinions.
Boutrous called the request for continued secrecy meritless, saying the court is able to unseal documents in the investigation that will lead to a judgment.
"This court need not question whether it has the 'authority' to determine whether material filed by the parties should be sealed or unsealed on its docket," Boutrous wrote. "To the contrary, this court has an independent obligation to determine whether sealing the record is warranted."
Boutrous said the court needs to take a narrow approach when deciding what information, if unsealed, should remain redacted from public view.
The attorney for the Wisconsin Club for Growth didn't immediately respond to a request for comment on Wednesday's motion.
Randa halted the investigation earlier this month, saying that the Wisconsin Club for Growth's free speech rights were violated by the probe. Prosecutors appealed that ruling and requested a stay in the 7th U.S. Circuit Court of Appeals, which has not yet ruled on the request.