Federal prosecutors are investigating Deutsche Bank’s role in a scheme that looted a Malaysian government fund, drawing the troubled German bank into a scandal that has already ensnared an American competitor, Goldman Sachs.

Deutsche Bank released a statement on Wednesday saying it had cooperated fully with all inquiries related to the fund, 1Malaysia Development Berhad, or 1MDB.

According to a person with knowledge of the matter who was not authorized to speak publicly, the inquiry is focused on a former Deutsche Bank employee who worked with Tim Leissner, a former Goldman partner who pleaded guilty to bribery and money-laundering charges. Those charges stem from Mr. Leissner’s role in funneling money out of 1MDB, a state infrastructure fund that Malaysia’s former prime minister and some of his associates raided for personal use.

The investigation into Deutsche, first reported by The Wall Street Journal, adds to the bank’s many problems; it is under scrutiny for its links to a money-laundering scheme in Denmark, and for potentially failing to report suspicious transactions by President Trump’s son-in-law, Jared Kushner. The bank announced on Monday that it would lay off 18,000 people around the world as part of a huge restructuring that will sharply shrink its Wall Street presence.