The note, which the newspaper claims was sent on Epstein's 50th birthday, has been called "fake" by Trump.
Now, in a social media post, Trump writes: "I look forward to getting Rupert Murdoch to testify in my lawsuit against him and his 'pile of garbage' newspaper, the WSJ. That will be an interesting experience!!!"
Trump previously said the newspaper and owner Rupert Murdoch "were warned directly" they would be sued if they printed the story, describing it as "false, malicious, and defamatory".
His Attorney General Pam Bondi says they are ready to unseal grand jury transcripts on Friday - but it could take some time for a judge to release the documents
Elsewhere, the Wall Street Journal reports Trump's name appeared on a "bawdy" 2003 personal note to Epstein - the president calls it "fake"
Trump threatens to sue media tycoon Rupert Murdoch and the newspaper over the story, describing it as "false, malicious, and defamatory"
During his presidential campaign, Trump promised to release files relating to Epstein
He faces mounting pressure from his own supporters and US media after Bondi said the US justice department did not believe Epstein had a so-called client list
Members of the US House of Representatives could be asked to vote on whether to release the documents relating to the prosecution of Jeffrey Epstein.
Representatives Thomas Massie (Kentucky's Republican representative) and Ro Khanna (California's Democrat representative) have proposed a so-called "discharge petition", which has been dubbed the "Epstein Files Transparency Act".
It would require Attorney General Pam Bondi to "make publicly available in a searchable and downloadable format all unclassified records, documents, communications, and investigative materials in the possession of the Department of Justice, including the Federal Bureau of Investigation and United States Attorneys’ Offices” relating to Epstein.
The proposed resolution has already gained the support of 15 bipartisan co-sponsors, external, including Republican Marjorie Taylor Greene and Democrat Alexandria Ocasio-Cortez.
To bypass House leadership the petition needs to reach 218 signatures - however, the Congress website notes that "discharge is designed to be difficult to accomplish and has rareDonald Trump is facing an unusual amount of pressure from his own supporters to release documents on Jeffrey Epstein.
One Republican pressure group has even resorted to pushing its message on a Times Square billboard.
"Why won't Trump release the Epstein files? Americans want answers," a huge ad from Republican Accountability in the popular New York hotspot reads.
In a statement, the Republican pressure group suggests that Trump "is trying to shut this down by ordering Republicans to stop asking questions about the Epstein files".
"But the more he rants, the more Americans want to know what his administration is hiding," the statement adds.
A billboard in Times Square that asks Trump, why won't you release the Epstein files? Images of Epstein and newspaper clippings on screen as buildings stand tall behind the advert.
The demands for the Trump administration to release Jeffrey Epstein files has sent Washington into a frenzy.
But on the ground in north-east Pennsylvania, Trump's supporters believe their president would ultimately handle the situation.
Vice-President JD Vance visited the town of West Pittston this week, and received a warm welcome from supporters.
"When he's ready, he'll let them out," Ed DeLucca, 72, tells me. He says he hopes Trump will bring the documents to light.
"There's a reason for it," he adds on the delay. "They'll come out."
Voters like Chrissy Matticks were far more focused on the economy and the border, and gave the president high marks for his policies - including the controversial roundups and deportations of undocumented immigrants.
"I'd say, to our Maga base: Have faith in President Trump," she tells me.
That's not to say everyone in West Pittston was sanguine about the files. Steven Taylor, a truck driver, told BBC's US partner CBS News that Trump needed to prioritise the release of the files.
"We didn't ask for it. And now we want it. We demand it."ly been used successfully".
"My father has a very specific way of speaking. People all over the world have mimicked it for decades," Donald Trump Jr says in a post on X.
He's coming to the defence of his father, over the Wall Street Journal article which alleges Trump sent a lewd personal birthday note to Epstein in 2003.
It reportedly contains a joking reference that “enigmas never age” and allegedly ends with the words: "A pal is a wonderful thing. Happy Birthday – and may every day be another wonderful secret."
The newspaper says the card allegedly had a lewd drawing in it, done by heavy marker.
"The insanity written in the Wall Street Journal, AIN’T IT and everyone knows it. Also in 47 years I’ve never seen him doodle once. Give me a break with the fake 'journalisming'", Trump Jr adds in response.
He is quoting a post that says Trump has never used the word "enigma" before, however video footage shows him saying the word in 2015.
