The Manhattan district attorney's office blasted House Republicans in a letter dated Friday.
Three committee chairmen have subpoenaed DA Bragg over the office's investigation into Trump.
"What neither Mr. Trump nor Congress may do is interfere with the ordinary course of proceedings in New York State," the DA's general counsel, Leslie Dubeck, added.
In the aftermath of the indictment, he rallied his congressional Republican allies, who had been trying to investigate the Manhattan district attorney's office, for support, according to CNN.
Friday's letter says any interference in an ongoing criminal investigation would be "unprecedented and illegitimate," and jeopardize Trump's privacy rights.