Lawyers for five men alleged to have been behind the 11 September 2001 attacks on the US have argued that their death penalty trial is so important it should be televised globally.
The issue of televising the proceedings was discussed on the final day of a week-long pre-trial hearing for Khalid Sheikh Mohammed and four co-defendants, who are accused of plotting the attacks.
US Defence Secretary Leon Panetta has sole authority to authorise the broadcast of the trials.
A Pentagon spokesman said that nobody has formally asked him to do so.
"If these proceedings are fair, why is the government afraid to let the world watch?" asked Marine Major William Hennessy, a US military lawyer defending Walid Bin Attash, a Yemeni accused of training two of the hijackers at an al-Qaeda camp in Afghanistan.
"The government admits that these are historic proceedings," Maj Hennessy added.
However, the prosecution said the trial should not become "reality TV".
Currently, the public can watch closed-circuit broadcasts of the Guantanamo war crimes court proceedings only at a 200-seat theatre at Fort Meade, a US Army base in Maryland.
Closed-circuit viewing sites at a handful of other military bases in the eastern United States are restricted to relatives of the 2,976 people killed in the 11 September attacks and to the firefighters, police officers and other emergency responders who gave aid and searched for victims at the crash sites in New York, Washington and Pennsylvania.
In hearings at the remote US naval base at Guantanamo Bay, Cuba, lawyers for some of the defendants asked the judge to open those viewing sites to the general public, which the judge declined to do.
Lawyers for other defendants said the trial should be televised globally to anyone who wants to watch.
The prosecution said the right to an open trial provided by the US Constitution has been satisfied by the Fort Meade viewing site, and that no one who wanted to watch the hearings there has been turned away.
Officials at Fort Meade have said during previous hearings that only a few dozen people turned up to watch, and that most of them were journalists or lawyers assigned to other Guantanamo cases.