President Trump and his administration want to move on from Jeffrey Epstein, the disgraced financier and sexual offender, who once associated with some of the world’s richest and most powerful people. Some of Mr. Trump’s most loyal supporters insist there is more to uncover.

But it’s not just the MAGA faithful who are refusing to let it go.

Senator Ron Wyden of Oregon, the top Democrat on the powerful Senate Finance Committee, has been digging into Mr. Epstein’s financial network for the past three years. Some members of his staff have viewed confidential files that shed light on the immense sums of money that, they say, Mr. Epstein moved through the banking system to fuel his vast sex-trafficking network.

In particular, filings by four big banks flagged more than $1.5 billion in transactions — including thousands of wire transfers for the purchase and sale of artwork for rich friends, fees paid to Mr. Epstein by wealthy individuals, and payments to numerous women, the senator’s office found. The filings came after Mr. Epstein was arrested in 2019 on federal sex trafficking charges.

Large money transfers to individuals, foreign countries or obscure companies are the kind of things banks are supposed to be examining as potentially suspicious. Some of the Epstein money transfers disclosed in a report from JPMorgan Chase involved accounts at two Russian banks before those institutions were subject to U.S. sanctions. A few transactions red-flagged were for as much as $100 million.

Mr. Wyden said his investigation into Mr. Epstein’s finances had taken on new urgency now that the Trump administration was balking at releasing any of the information seized by the F.B.I. from Mr. Epstein’s homes or information collected from the nation’s banks. Like many Republicans on the far right, Mr. Wyden and a growing number of Democrats believe there are more details about Mr. Epstein that the federal government needs to reveal.

“We felt from the beginning this was a follow-the-money case,” Mr. Wyden said in an interview. “This horrific sex-trafficking operation cost Epstein a lot of money, and he had to get that money from somewhere.”

The bank records reviewed by Mr. Wyden’s staff — called suspicious activity reports or S.A.R.s — are meant to be an early warning system for law enforcement about signs of illegal activity. As dictated by federal law, the reports are so confidential that banks can’t even acknowledge filing them, and people who have seen the documents are under great constraint as to what they can say about them.

Members of Mr. Wyden’s staff provided an overview of the banks’ reports to The New York Times based on their review of the filings.

To some degree, Mr. Wyden is hamstrung by those rules, which is why he wants the Trump administration to make the reports available to Congress so members can review them and possibly issue subpoenas to the banks for more information.

Even before the Justice Department announced last week that it was closing the door on the Epstein investigation, Mr. Wyden had been pressing Attorney General Pam Bondi to turn over bank reports along with other information about wealthy individuals and financial institutions in Mr. Epstein’s network.

Mr. Trump, who was once friendly with Mr. Epstein, said this week that he would let Ms. Bondi decide which documents should be made public. He also dismissed his supporters who are calling for the release of Epstein-related files and said the matter was old news.

The Justice Department did not respond to a request for comment. Ms. Bondi has said she stands behind the department’s memo that said “no further disclosure” of information was warranted.

The banks that filed reports reviewed by Mr. Wyden’s team — JPMorgan, Bank of America and Bank of New York Mellon — all declined to comment except for Deutsche Bank, which said it “regrets our historical connection with Jeffrey Epstein.”

The confidential bank reports filed with a Treasury Department agency could be crucial, because they provide the most comprehensive look at the enormous financing machine behind Mr. Epstein’s sex-trafficking operation in Manhattan, Florida and the U.S. Virgin Islands. To date, only bits and pieces of the financial transactions involving Mr. Epstein’s network have come out through civil litigation and news reports.

“In this era of misinformation, these reports are the coin of the realm,” Mr. Wyden said of the confidential bank reports.

The reports reviewed by Mr. Wyden’s team were filed by the banks months after Mr. Epstein’s arrest in 2019 on federal sex-trafficking charges and his subsequent death by suicide in a federal jail in Manhattan.

Normally, a bank is expected to file a suspicious activity report within 60 days of a bank’s spotting a questionable transaction, such as movements signaling money laundering or sex trafficking.

Gary Kalman, executive director for the U.S. arm of Transparency International, which focuses on illicit financing, said banks have to make a lot of assessments about a client before deciding to file S.A.R.s, including reading news reports.

In 2008, Mr. Epstein pleaded guilty in Florida to a charge of soliciting prostitution from a teenage girl and received a modest jail sentence.

In conjunction with the guilty plea, federal prosecutors in Florida entered into a deal with Mr. Epstein that required him to register as a sex offender but not to prosecute him separately. The deal was criticized by victims, because authorities had reports that Mr. Epstein had sexually abused dozens of teenagers.

Many of the wealthy men, celebrities and politicians who associated with Mr. Epstein over the years have said in interviews or statements that they were unaware of the extent of his wrongdoing until he was arrested a second time in 2019.

It is unclear if more frequent and timely S.A.R.s filings would have made much of a difference with law enforcement given the years of criticism over how authorities handled Mr. Epstein’s investigation.

Still, Mr. Wyden said the reporting system needed fixing, especially as it pertains to monitoring wealthy banking clients.

“When banks are only filing these reports after crooks like Epstein are dead or behind bars, that does not do anyone any good,” he said.

Mr. Wyden began his investigation roughly three years ago, with a particular focus on the more than $158 million in payments the billionaire investor Leon Black made to Mr. Epstein for tax and estate planning services. Mr. Black, who socialized with Mr. Epstein, was a co-founder of the private equity firm Apollo Global Management.

In early 2021, Mr. Black stepped down from all leadership posts at the firm after those payments and his close ties to Mr. Epstein became public. Mr. Black’s legal team has said that Mr. Epstein’s work saved Mr. Black some $2 billion in taxes and that he did nothing wrong in paying Mr. Epstein.

Early last year, his investigators, along with several Republican committee staffers, were permitted by Treasury officials to review the secret filings by the four banks.

The staff members were presented with thousands of pages of documents to review. But they were not allowed to make copies and could take only handwritten notes.

The single largest suspicious activity report reviewed by the congressional team was filed in late 2019 by JPMorgan for $1.1 billion. The report covered 4,700 transactions dating to 2003, including payments to women from Belarus, Russia and Turkmenistan. Many of Mr. Epstein’s victims included young women from Eastern European countries.

The next largest was by Deutsche Bank for about $400 million, followed by Bank of New York Mellon for $378 million and then Bank of America, which filed reports on Mr. Black’s payments to Mr. Epstein.

In 2023, JPMorgan paid $290 million to Mr. Epstein’s victims and Deutsche paid $75 million to settle lawsuits that claimed the banks ignored red flags about potential sex trafficking.

Marijke Chartouni, who was sexually abused by Mr. Epstein when she was 20, said the furor between Mr. Trump and his supporters had obscured the harm done to victims. Ms. Chartouni, who is now 45, also said law enforcement was to blame for not having more aggressively pursued Mr. Epstein and his network.

“Sadly, all this noise around the purported ‘Epstein Files’ serves only to detract from holding the Justice Department accountable to victims for its failure in preventing this trafficking atrocity,” she said in an interview.