The Manhattan district attorney’s office on Monday accused President Trump and his lawyers of trying to invent a “new presidential ‘tax return’ privilege” by arguing that Mr. Trump should not have to comply with a subpoena seeking eight years of his personal and corporate returns.

The district attorney’s office used the pointed language in court papers, asking that a lawsuit filed by Mr. Trump last week be dismissed. Mr. Trump sued in federal court to block a subpoena issued by the district attorney, Cyrus R. Vance Jr., to the president’s accounting firm that seeks his tax returns dating to 2011.

Citing constitutional grounds, lawyers for Mr. Trump argued in their lawsuit that a sitting president could not be criminally investigated and said that forcing him to comply with the subpoena would cause him “irreparable harm.”

In its response, the district attorney’s office noted that Mr. Trump did not go to court to stop two recent criminal investigations that focused on him or his family business, one by the special counsel, Robert S. Mueller III, and the other by federal prosecutors in Manhattan.