More than a dozen mainstream media news organizations petitioned the federal judge Tuesday to allow broadcast and webcast of closing arguments in the Proposition 8 lawsuit “to enhance the public’s ability to witness the parties’ respective closing arguments in this historic case.”

In a letter to U.S. District Court Judge Vaughn Walker, the news groups ask Walker to once again ask 9th Circuit U.S. Court of Appeals Chief Judge Alex Kozinski for permission to include closing arguments under the circuit’s pilot project on broadcast of court proceedings.

The letter was delivered to Walker on behalf of NBC and CBS, Fox News, Associated Press, National Public Radio, the Cable News Network, In Session (formerly known as Court TV), and other large media interests.

The unprecedented interest in the case challenging California’s same-sex marriage ban prompted Walker to seek approval for some limited live broadcast of the proceedings—and delayed viewing on YouTube.com. But before the trial got underway, in January, the U.S. Supreme Court intervened and prohibited Walker from making a broadcast of the proceedings available anywhere outside the federal courthouse in San Francisco.

The 5 to 4 majority of the Supreme Court indicated its decision to bar broadcast of the Perry v. Schwarzenegger trial was based—not on the merits of whether this trial should be made available for public viewing, but rather because— “it appears the courts below did not follow the appropriate procedures set forth in federal law before changing their rules to allow such broadcasting.” Specifically, the majority suggested that Walker allowed only five business days for public comment on his plan to make the proceedings public, whereas “administrative agencies…usually” provide 30 days or more.

In their letter to Walker, the news organizations note that the federal district court has, since that time, re-opened the public comment period for 30 days and set forth the rules to authorize “the taking of photographs, public broadcasting or televising, or recording” court proceedings as part of the 9th Circuit’s pilot project. The news groups say they believe those developments make broadcast of closing argument “consistent with federal law” and the Supreme Court’s initial ruling.

The groups also note that earlier objections by defendants that broadcast of the proceedings could make them vulnerable to criticism or harassment from people who disagree with them are not at issue in the closing arguments since only attorneys will be speaking in court.

As of Tuesday night, Walker had not yet indicated whether he would seek approval for the broadcast.

Closing argument is scheduled for June 16.