Representative Frederica Wilson said he had told Myeshia Johnson: "He knew what he was signing up for, but I guess it hurts anyway."
Mr Trump said Ms Wilson's account was "totally fabricated".
Sgt La David Johnson was killed in Niger by Islamist militants this month.
He was one four US special service soldiers who died in an ambush.
Mr Trump had already been criticised for not contacting the families of the dead servicemen right after the fatal ambush on 4 October.