It will cost the New York Police Department significantly less to provide presidential protection and to guard Trump Tower than the city had initially estimated, according to the police commissioner, James P. O’Neill.

In a letter to members of the New York delegation to Congress seeking reimbursement for the Police Department’s expenses, Commissioner O’Neill noted that it had cost the police about $24 million to provide security to President Trump and his family in New York as well as to guard Trump Tower during the two and a half months between Election Day and Inauguration Day — a figure well below the $35 million that the police had initially estimated.

The letter, dated Tuesday, includes detailed estimates about the Police Department’s expenses associated with presidential security. On days when Mr. Trump is not in the city, the department estimates that it costs $127,000 to $146,000 a day “to protect the first lady and her son while they reside in Trump Tower.” On days when Mr. Trump is in New York City — he has not yet returned since his inauguration — the Police Department anticipates “an average daily rate of $308,000.”

That would come out to about $50 million a year if Mr. Trump avoided returning to Manhattan, or just over $60 million if he began returning on weekends.