Michael L. Cohen, who led Och-Ziff’s investments in Africa, is referred to in court filings without his name being used. Mr. Cohen left the firm in 2013. He was also an officer in Africa Management Ltd., a joint venture set up by Och-Ziff to secure African resource contracts. Mr. Cohen worked closely at Och-Ziff with a former associate, Vanja Baros, who is also referred to in court filings from prosecutors but is not named.

A representative for Mr. Baros declined to comment on Thursday. Ronald G. White, Mr. Cohen’s lawyer, said his client had “an unblemished reputation built over the course of a career spent creating value for Och-Ziff’s investors,” adding that he had “done nothing wrong.”

Mr. Frank also declined to comment.

The settlement focuses attention on one of the biggest and best-known hedge funds and one of the few publicly traded firms in the opaque $3 trillion hedge fund universe.

“This has been a deeply disappointing episode,” Mr. Och said in an emailed statement, adding: “This conduct is inconsistent with our core values and not representative of our hundreds of employees worldwide, who are dedicated to serving our clients with the utmost integrity. We have learned from this experience and taken significant steps to strengthen Och-Ziff.”

Between 2007 and 2011, Och-Ziff pushed ahead with deals even though some within the firm raised questions about whom it was dealing with in Africa, according to the government.

The S.E.C., for instance, said in its administrative order that Mr. Och and Mr. Frank “were aware of corruption accusations” against one partner it was working with in Congo. But the S.E.C. added that neither Mr. Och nor Mr. Frank knew that bribes would be paid.

In another instance, an unidentified employee at Och-Ziff emailed Mr. Och to describe an important meeting with Libyan officials, including one of Qaddafi’s sons, in Vienna in 2007.