A coalition of media organizations, including CNN, is asking the federal court in Washington, DC, to give more transparency into the legal fight over a search warrant special counsel Jack Smith obtained for materials from former President Donald Trump's Twitter account.

The news outlets are asking for the court to unseal the materials that prosecutors filed when applying in January for the warrant, which was sought as part of Smith's 2020 election subversion investigation.

Twitter -- which has since been rebranded as X -- did not object to the warrant itself, according filings from appeals court proceedings in the dispute that were unsealed earlier this month, but fought against an order barring the platform from telling Trump about the warrant.

The new request from the media organizations is also seeking for the unsealing underlying docket in the district court case -- which remains inaccessible to the public -- and for the release of court filings or orders that sought for or permitted for the case to be sealed, as well as "all other judicial records, including any audio recordings of any hearings, as to which there is no longer a compelling need for secrecy."

"The First Amendment and common law rights of access to court records are 'a fundamental element of the rule of law, important to maintaining the integrity and legitimacy of an independent Judicial Branch,'" the media outlets wrote in their new filing, while quoting from a DC Circuit opinion written by then-Circuit Judge Merrick Garland. "Nowhere is the maintenance of integrity and legitimacy more important than in a case like this one, involving the historic and closely-watched investigation of a former President."

The Justice Department opposes the unsealing request, the media organizations said in the new court filings.

The warrant, and the legal fight that followed, was revealed with the recent release of a July opinion from the US DC Circuit Court of Appeals, which upheld sanctions levied by the district court against Twitter for the platform's delay in producing the records investigators were seeking. Over the course the litigation, the order prohibiting disclosure of the warrant to Trump was amended so that Twitter could tell him some things about the warrant, the appeals court opinion said.

Much is still unknown about what of Trump's Twitter data investigators were seeking, and why they had sought the search. But transcripts released last week of February proceedings in front of Judge Beryl Howell, then the chief judge of the DC district court, indicated that investigators sought private direct messages -- of which there were many -- from the former president's account. The appeals court has since given the parties an August 30 deadline to explain why certain other filings as well as audio from other court hearings related to the dispute shouldn't be released.

With the new request that additional court records related to the warrant be unsealed, the media organizations noted that Trump has since been indicted in Smith's probe, and that existence of the warrant has already been made known by the court documents released by the appeals court.

"Indeed, at this point it is difficult to imagine any justification for continued sealing," the news organizations said.

The outlets' lawyers conferred Monday with X's counsel, according to the new filing, and X consented to the request but asked for two categories of redactions. One category of redactions -- which would hide the name of a senior counsel for the platform who signed a declaration -- the media organizations do not oppose. The press coalition however does oppose a request from X that the email account associated with @realDonaldTrump be redacted.