Her casket was placed on the Lincoln Catafalque, once used for President Abraham Lincoln, before a ceremony inside the court's Great Hall attended by family, friends and her fellow justices, all wearing masks.
Chief Justice John Roberts spoke, calling her a "fighter" for equal justice and saying "her voice was soft, but when she spoke, people listened."
Roberts, who sat next to Ginsburg on the Supreme Court bench, said her life was a reflection of the American Dream, noted her love of opera and called her "a star" who "found her stage in our courtroom."
One of her "many virtues" that defined her time on the bench, he said, was her "humility."
"The court was her family, too. This building was her home," he said. "Ruth is gone and we grieve."
"May she rest in peace," Roberts said, standing in front of a portrait of Ginsburg.
Then, in an unprecedented move, because of the pandemic, her casket was brought outside and placed at the top of the court steps under the portico so members of the public could pay their respects.
There has been an outpouring of public support at the court since word of Ginsburg's death at age 87 came Friday night. With warm, sunny weather in Washington on Wednesday, large crowds were expected.
Some of those who came to honor her wore "Notorious RBG" shirts, the nickname she became known by to her devoted supporters.
Many who gazed at her flag-draped casket from the bottom of the court steps were women and girls.
Mourners had started to gather early Wednesday morning near the court steps, where there had been a makeshift memorial of flowers and messages in remembrance of the impact she has had on people's lives in her almost 30 years as a liberal icon on the nation's high court.
The memorial, which wrapped around the building, was cleared away overnight -- some was collected by the court curator and other items were donated to Ginsburg's family or interested museums.
Ginsburg will lie in repose at the Supreme Court through Thursday. The public outdoor viewings continue Wednesday until 10 p.m. and resume Thursday from 9 a.m. until 10 p.m.
The White House announced that President Donald Trump would go to the court Thursday to pay his respects.
Among those paying their respects on Wednesday were Vice President Mike Pence, second lady Karen Pence, former Secretary of State Hillary Clinton and former President Bill Clinton -- who nominated Ginsburg to the bench in 1993.
On Friday, Ginsburg will lie in state at the Capitol, the first woman in U.S. history to be so honored, at the direction of House Speaker Nancy Pelosi.
Nearby in the Capitol, a bitter political battle continued over her replacement.
She will be interred next week beside her husband of 56 years at Arlington National Cemetery.
ABC News' Devin Dwyer contributed to this report.