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The flag-draped casket carrying Scalia's body arrived at the court just before 9:30 a.m. and was carried slowly up the steps by court police, who served as pallbearers, and passed through two lines of former clerks, who served as honorary pallbearers.
The other justices stood in a receiving line inside the Great Hall, standing solemnly as the casket was laid on the same catafalque upon which President Abraham Lincoln’s casket once rested.
Following a private ceremony, the court opened to the public at 10:30 a.m. and is set to remain open until 8 p.m.
Throughout the day, four former clerks to the late justice will stand watch by the casket at all times, circulating through in 30-minute shifts.
President Obama and first lady Michelle Obama paid their respect this afternoon.
The president in a dark suit and the first lady also in black, the couple bowed their heads in front of Scalia’s casket in silence for several moments before walking over to a portrait on display, talking between themselves.
At the time the court opened to the public, the line stretched down the block. Among those in line were students in town on Washington trips, hoping to witness a piece of history, and members of the public and legal community hoping to honor Scalia’s memory and his contributions to the law with their visit.
Two high school students from North Carolina were the first in line, arriving at 6:50 this morning.
"It was very moving," said Emily Weatherspoon, 17, who was one of the first in line this morning and is visiting Washington with her high school class from North Carolina.
Melissa Covey, a legal assistant from Virginia, was in line behind the teenagers and said she wanted to pay her respects to a man she views as a legal giant.
"Justice Scalia is my hero in the Supreme Court,” Covey said.
A funeral service for family and friends will be held Saturday at the Basilica of the National Shrine of the Immaculate Conception in Washington, D.C., at 11 a.m.
The president will not attend the Saturday service, but Vice President Joe Biden and his wife will be in attendance. The burial, at a location that has not been announced, will be private.
In keeping with court tradition dating back to 1873, Scalia's place on the bench, his chair and the bench directly ahead of his seat, have been draped in a black wool crepe since Tuesday. A black drape also hangs above the doors to the court.
The last justice to lie in repose at the court was Chief Justice William Rehnquist, who died in 2005.
ABC News' Geneva Sands contributed to this report.