The congressional investigations are focused on Deutsche Bank’s close relationship with Mr. Trump and his family. Over the past two decades, it was the only mainstream financial institution consistently willing to do business with Mr. Trump, who had a history of defaulting on loans. The bank lent him a total of more than $2 billion, about $350 million of which was outstanding when he was sworn in as president.

Two House committees have subpoenaed Deutsche Bank for records related to Mr. Trump and his family, including records connected to the bank’s handling of potentially suspicious transactions. The president has sued to block Deutsche Bank and Capital One, where he also holds money, from complying with the subpoenas. A federal judge rejected Mr. Trump’s request for an injunction, and the president has appealed that ruling.

The Justice Department has been investigating Deutsche Bank since 2015, when agents were examining its role in laundering billions of dollars for wealthy Russians through a scheme known as mirror trading. Customers would use the bank to convert Russian rubles into dollars and euros via a complicated series of stock trades in Europe and the United States.

In early 2017, federal and state regulators in the United States and British authorities imposed hundreds of millions of dollars in civil penalties on Deutsche Bank for that misconduct, but prosecutors never brought a criminal case against the bank. That led some senior Deutsche Bank executives to believe they were in the clear, according to people familiar with their thinking.

By last fall, though, federal agents were investigating a wider range of anti-money-laundering lapses and other possible misconduct at the bank.

F.B.I. agents met this year with Val Broeksmit, whose father was a senior Deutsche Bank executive who committed suicide in January 2014. Mr. Broeksmit said he had provided the agents with internal bank documents and other materials that he had retrieved from his father’s personal email accounts.