Kerrie McHugh, a Deutsche Bank spokeswoman, said the company had intensified its efforts to combat financial crime. An effective anti-money laundering program, she said, “requires sophisticated transaction screening technology as well as a trained group of individuals who can analyze the alerts generated by that technology both thoroughly and efficiently.”

“At no time was an investigator prevented from escalating activity identified as potentially suspicious,” she added. “Furthermore, the suggestion that anyone was reassigned or fired in an effort to quash concerns relating to any client is categorically false.”

Amanda Miller, a spokeswoman for the Trump Organization, the umbrella company for the Trump family’s many business interests, said: “We have no knowledge of any ‘flagged’ transactions with Deutsche Bank.” She said the Trump Organization currently has “no operating accounts with Deutsche Bank.” She did not respond when asked if other Trump entities had accounts.

Karen Zabarsky, a spokeswoman for Kushner Companies, said: “Any allegations regarding Deutsche Bank’s relationship with Kushner Companies which involved money laundering is completely made up and totally false. The New York Times continues to create dots that just don’t connect.”

Deutsche Bank’s decision not to report the transactions is the latest twist in Mr. Trump’s long, complicated relationship with the German bank — the only mainstream financial institution consistently willing to do business with the real estate developer.

Congressional and state authorities are investigating that relationship and have demanded the bank’s records related to the president, his family and their companies. Subpoenas from two House committees seek, among other things, documents related to any suspicious activities detected in Mr. Trump’s personal and business bank accounts since 2010, according to a copy of a subpoena included in a federal court filing.

Mr. Trump and his family sued Deutsche Bank in April, seeking to block it from complying with the congressional subpoenas. The president’s lawyers described the subpoenas as politically motivated.