In late-night court filings on Tuesday, US federal prosecutors said unsealing the materials would be appropriate given the "abundant public interest" in the case of Epstein, the late financier, and Maxwell, an imprisoned British socialite.
The Republican Trump had promised to make public Epstein-related files if re-elected and accused Democrats of covering up the truth. But earlier in July, the Department of Justice said a previously touted Epstein client list did not exist, angering Trump's supporters.
Democrats are also pushing for the release of Epstein files, saying Trump should be held accountable for breaking his promise to release them.
US Senate Minority Leader Chuck Schumer and a group of his fellow Democrats said they have invoked a century-old law to compel the Justice Department to release a broad range of Epstein documents while protecting the privacy of victims.
Asked whether Tuesday's letter to Attorney-General Pam Bondi included the release of grand jury transcripts, Schumer told reporters, "Well, that will have to be litigated."
It was unclear whether the Justice Department would aim to respond by the August 15 deadline that the Democrats set.
The DOJ first sought court permission on July 18 to make public transcripts of the confidential testimony given by witnesses years ago in the two cases, but Manhattan-based US District Judges Richard Berman and Paul Engelmayer asked the government to flesh out the legal bases for the requests.
Trump has faced pressure to make public documents from the federal investigations into Epstein, who took his own life in 2019 while awaiting trial on sex trafficking charges, and his longtime girlfriend Maxwell, who was convicted of sex trafficking in 2021.
Even if one or both of the judges allow the transcripts to be made public, it is unclear whether the public would learn anything new or noteworthy.
In the filings, prosecutors said the only witness at Epstein's grand jury was an FBI agent. That same agent and a New York City Police Department detective were the only witnesses at Maxwell's grand jury, prosecutors said.
Maxwell's four-week trial in 2021 included public testimony from alleged sex trafficking victims, associates of Epstein and Maxwell, and law enforcement officers.
She is serving a 20-year prison sentence in Florida and is asking the US Supreme Court to overturn her conviction. She had pleaded not guilty.
The unsealing requests came after Trump earlier in July asked Bondi to seek the release of grand jury transcripts. The president did so after the Justice Department said it concluded that Epstein died by suicide and that there was no incriminating list of his clients.
The Justice Department's announcement angered some of Trump's conservative supporters who believe the government is covering up Epstein's ties to the rich and powerful and that the financier was murdered in jail.
The transcripts would not represent all previously unreleased material in the government's possession. Investigators and prosecutors may pursue leads that they cannot substantiate or interview potential witnesses whom they do not ultimately call to testify before a grand jury.
Epstein pleaded guilty in 2008 to a prostitution charge brought under Florida law and was given a 13-month sentence in a deal with prosecutors now widely regarded as too lenient.
Deputy US Attorney-General Todd Blanche, Trump's former personal lawyer, last week met with Maxwell to see if she had any information about others who had committed crimes. Maxwell's lawyer, David Markus, and Blanche have not provided detailed accounts of their discussions.
