Pete Marovich/European Pressphoto Agency

When Timothy F. Geithner ran the Federal Reserve Bank of New York, he acknowledged fundamental problems with the process for setting key interest rates in the midst of the 2008 financial crisis, according to documents provided to The New York Times.

Mr. Geithner, who is now the United States Treasury secretary, questioned the integrity of the benchmark as reports surfaced that Barclays and other big banks were misrepresenting the rates. In 2008, Barclays had several conversations with New York Fed officials about the matter.

Mr. Geithner then reached out to top British authorities to discuss issues with the interest rate, which is set in London. In an e-mail to his counterparts, he outlined reforms to the system, suggesting that British authorities “strengthen governance and establish a credible reporting procedure” and “eliminate incentive to misreport,” according to the documents.

But the warnings came too late, and Barclays continued the illegal activity.

For years, Barclays reported false rates in an effort to bolster its profit and deflect concerns about the British bank’s health. Last month, the bank agreed to pay $450 million to American and British authorities to settle claims that it had manipulated key benchmarks, including the London interbank offered rate, or Libor.

Libor and other such rates affect the cost of borrowing for consumer and companies, providing a benchmark for trillions of dollars in mortgages and other financial products. The case against Barclays is the first action to stem from a broader multiyear investigation into how big banks set the rates. Authorities around the world are pursuing investigations against more than 10 big banks, including UBS, JPMorgan and Citigroup.

Since the Barclays settlement, regulators have faced scrutiny of their roles in the rate-manipulation scandal.

Lawmakers in London and Washington have questioned whether government officials turned a blind eye to years of misconduct at Barclays. The bank has disclosed that it informed regulators, including the Bank of England and the Federal Reserve Bank of New York, that it had reported artificially low rates, along with the rest of the Wall Street.

This week, the oversight panel of the House Financial Services Committee sent a letter to the New York Fed seeking transcripts from several phone calls involving regulators and Barclays’ executives. The New York Fed plans to release the transcripts on Friday.

Mr. Geithner is not mentioned in the transcripts, a person briefed on the matter said who did not want to be identified because the investigation was continuing. But it is unclear if other documents will detail whether he had deeper knowledge of the issues with Libor, and what further actions — if any — Mr. Geithner took. According to the person briefed on the matter, New York Fed officials told regulators in Washington about the problems with Libor.

The New York Fed, which oversees the holding company at some of the nation’s biggest banks, first got wind of brewing problems with Libor in the summer of 2007. At the time, Barclays executives started briefing the regulators in the United States and Britain about their interest rate submissions.

In April 2008, a Barclays employee acknowledged to the Financial Services Authority of Britain that the bank was lowering its Libor submissions. “So, to the extent that, um, the Libors have been understated, are we guilty of being part of the pack? You could say we are,” the Barclays manager said, according to regulatory documents. Barclays made similar comments to the New York Fed, the documents say.

The bank never explicitly told regulators that it was reporting false interest rates that amounted to manipulation, according to regulatory documents.

In Basel, Switzerland, Mr. Geithner discussed the Libor with Mervyn King, the governor of the Bank of England, Britain’s central bank, according to the documents provided to The New York Times. Mr. Geithner then followed up with a June 2008 e-mail to Mr. King, outlining in a two-page memo his suggested changes to the way big banks set the interest rate, a copy of the memo shows. Mr. Geithner made six main recommendations for “enhancing the credibility of Libor.”

“We would welcome a chance to discuss these and would be grateful if you would give us some sense of what changes are possible,” Mr. Geithner wrote.

Mr. King responded “favorably” the person briefed on the matter said. The person added that the respective regulators continued discussions.

Documents released by the Bank of England on Friday show that Mr. King and Paul Tucker, the central bank’s deputy governor, passed on Mr. Geithner’s recommendations to the British Bankers’ Association, the trade body that oversees the Libor rate.

Mr. Tucker also talked to William C. Dudley, the current president of the Federal Reserve Bank of New York, who was the executive vice president of the central bank’s markets group at the time of the discussion.

In a separate note, Angela Knight, the chief executive of the British Bankers’ Association, told Mr. Tucker that the suggestions from U.S. authorities were being included in a review of Libor. The trade body published its findings at the end of 2008, but is now conducting a further review into how the rate is set.

The memo from Mr. Geithner, however, raises new questions about why the Bank of England failed to halt the actions. At a hearing this week, British politicians hammered Mr. Tucker, the senior Bank of England official who is now a front-runner to become the next head of the bank, for failing to thwart the misconduct.