Manhattan District Attorney Cyrus Vance's office said the allegations against him were baseless But a spokeswoman for Mr Vance said the claims were "wholly without merit".
Meanwhile, Mr Strauss-Kahn's lawyers said they were not discussing a plea bargain, the New York Times reports.
"Mr Strauss-Kahn will not be pleading guilty to anything," defence lawyer William Taylor told the newspaper following a 90-minute private meeting with prosecutors.
The former IMF chief denies sexually assaulting a hotel maid in New York on 14 May, and was recently freed from house arrest in the city.
Credibility undermined Late on Wednesday, the lawyer for Mr Strauss-Kahn's accuser wrote to Mr Vance requesting he step down after leaking information revealing the prosecution's doubts about the 32-year-old Guinean maid's credibility.
Kenneth Thompson said he wanted to ensure his client's rights "are not further prejudiced by deliberate acts seeking to undermine her credibility".
Mr Thompson said Mr Vance should be replaced by a special prosecutor.
But the district attorney's office said the allegation was baseless.
Strauss-Kahn denies all charges Mr Strauss-Kahn had been a leading contender to be the French Socialist Party's presidential candidate before his arrest in May.
Concerns about the reliability of his accuser in New York have left that case reportedly in trouble, and led to speculation that he might return to French politics.
However, on Monday, Socialist Party spokesman Benoit Hamon said the idea that Mr Strauss-Kahn could now run for the presidency was "the weakest" of all possible scenarios.
On Tuesday, French writer Tristane Banon filed a complaint accusing Mr Strauss-Kahn of trying to assault her as she attempted to interview him in a Paris flat in 2003.
Mr Strauss-Kahn said he would sue Ms Banon for making false statements.
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