House Speaker Nancy Pelosi opened the ceremony saying "it is with profound sorrow and deep sympathy to the Ginsburg family that I have the high honor to welcome Justice Ruth Bader Ginsburg to lie in state at the capitol of the United States."
Ginsburg, a stalwart liberal on the high court since 1993, died last Friday at age 87.
Known simply as RBG, she was an icon to millions of Americans - especially young girls - after a long legal career built on fighting for gender equality.
Statuary Hall was adorned with black ribbons affixed to the colossal marble columns around the room's perimeter, surrounding the area where a catafalque holds Ginsburg's flag-draped coffin.
Democratic presidential nominee Joe Biden, who presided over Ginsburg's confirmation hearings as a senator in 1993, is among those who attended the Capitol for Friday's ceremony.