NEW YORK — Companies accused of aiding Bernard Madoff’s vast pyramid scheme have agreed to pay more than $1 billion to settle a fraud lawsuit, the trustee charged with recovering Madoff’s funds said Thursday.

More than a dozen investment funds and a former chief executive of Tremont Group — accused of running the second-largest Madoff “feeder fund” — signed on to the settlement, the trustee, Irving Picard, said in a statement.

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Tremont, a multibillion-dollar money management firm based in New York, funnelled investors’ cash to Madoff investment business while ignoring warning signs that he was running a giant fraud, according to Picard.

Also included in the settlement were Tremont’s parent companies, Oppenheimer Acquisition Corp., which runs the Oppenheimer family of mutual funds, and the Massachusetts Mutual Life Insurance Company.

“We believe this settlement… sends a strong message that the financial community cannot deliberately ignore indicia of fraud,” David Sheehan, a lawyer working for the trustee, said in the statement.

The settlement brings the total amount of funds that Picard has recovered from Madoff’s scheme to $8.6 billion. This month, a court permitted the first payment from the recovered monies to Madoff’s victims.

Picard has filed numerous lawsuits against those he alleged were complicit in the Madoff fraud, including Wall Street bank JPMorgan Chase and the owners of the New York Mets baseball team.

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Madoff, 72, is serving a 150-year prison term for masterminding what is considered one of the biggest pyramid schemes ever, which by his account took in $65 billion dollars before it was uncovered in December 2008.

His victims, who invested with him over more than two decades, included charities, major banks, Hollywood moguls and savvy financial players.