The statement was accompanied by an image of a masked suspect wearing gloves and a hooded sweatshirt, carrying an object.
The U.S. Capitol Police said Officer Brian D. Sicknick was injured "while physically engaging with protesters" during the Wednesday riot, later dying in hospital.
State Del. Derrick Evans was among several lawmakers from across the country who travelled to Washington, D.C., for election fraud demonstrations.
More than 90 people have been arrested in Washington and more arrests are likely.