Federal prosecutors pursuing the criminal case against the cryptocurrency mogul Sam Bankman-Fried said on Wednesday that they were dropping a charge that he violated campaign finance rules.

Mr. Bankman-Fried was charged with fraud and campaign finance violations in December after the sudden collapse of his company, the cryptocurrency exchange FTX. He was quickly extradited to the United States from the Bahamas, where FTX was based.

But in a court filing on Wednesday night, the prosecutors said the Bahamas had informed them that the nation’s government had not intended to extradite Mr. Bankman-Fried on the campaign finance charge.

“In keeping with its treaty obligations to the Bahamas, the government does not intend to proceed to trial on the campaign contributions count,” the prosecutors’ filing said.

The removal of the charge is a victory for Mr. Bankman-Fried’s legal team, which had argued that the United States mishandled the extradition process. And it follows the prosecution’s decision in June to proceed to a trial in October without pursuing five other charges that were added to Mr. Bankman-Fried’s indictment in the weeks after his extradition.

The authorities have said Mr. Bankman-Fried and others at FTX used customer deposits to make $90 million in campaign contributions to some 300 political candidates or political action committees. Months ago, prosecutors and bankruptcy lawyers for FTX began asking recipients of those donations to return them.

A spokesman for Mr. Bankman-Fried declined to comment. A spokesman for the U.S. attorney’s office in the Southern District of New York, which is prosecuting the case, did not respond to a request for comment.

In total, Mr. Bankman-Fried is now set to face seven charges at his trial in October, including accusations that he defrauded customers and lenders of FTX. Prosecutors have argued that he orchestrated a sweeping fraud, siphoning billions of dollars that customers had deposited with FTX to finance campaign contributions, charitable donations and real estate purchases.

Prosecutors are planning a second trial on the five charges that were withdrawn in June, including an accusation that Mr. Bankman-Fried bribed a foreign government. They said they had to postpone a trial on those counts while litigation over the extradition unfolded in the Bahamas.

John P. Fishwick Jr., a former U.S. attorney for the Western District of Virginia, said prosecutors still had “overwhelming evidence against Sam Bankman-Fried.” He added that the removal of the campaign finance charge could work to the government’s advantage by making it a simpler fraud case to present to a jury.

If convicted on the securities fraud and wire fraud charges, Mr. Bankman-Fried faces the prospect of being sentenced to dozens of years in prison.

It is not clear what impact the decision by prosecutors will have on others associated with Mr. Bankman-Fried, who are being investigated for campaign finance violations — including Nishad Singh, a former FTX executive who is a key cooperating witness.

In February, Mr. Singh, 27, became the third former top lieutenant of Mr. Bankman-Fried to plead guilty to a variety of charges and work with prosecutors. The company’s former director of engineering, he pleaded guilty to taking part in a scheme overseen by Mr. Bankman-Fried to funnel tens of millions in illegal campaign donations to mostly Democratic candidates and political action committees.

Andrew Goldstein, a lawyer for Mr. Singh, was not immediately available for comment.

Mr. Fishwick said Mr. Singh “has no valid reason to withdraw his guilty plea” on the campaign finance charge. Doing so is never an easy task, he added.

Ryan Salame, another former FTX executive, is also under investigation for making campaign finance contributions to mostly Republican candidates. Mr. Salame has not been charged with any wrongdoing.

But in April, federal agents showed up at his Maryland home to seize cellphones used by him and his girlfriend Michelle Bond, who ran a crypto lobbying group and campaigned unsuccessfully for Congress as a Republican from Long Island.

Jason Linder, a lawyer for the couple, was not immediately available for comment.