More than 6,000 mourners -- including members of Congress -- began streaming by to view Scalia's casket as the court opened its doors to the public at 10:30 a.m.
Earlier Friday, all the current Supreme Court justices attended a private ceremony led by Scalia's son, Father Paul Scalia, in the Great Hall.
In the afternoon, President Barack Obama and first lady Michelle Obama visited the court to honor Scalia. They were greeted by Chief Justice John Roberts and then met with members of Scalia's family, including Army Lt. Col. Matthew Scalia, the late justice's son, and his wife, Michelle, in the Solicitor General's office.
The President and first lady stayed for roughly 25 minutes.
Sri Srinivasan and Patricia Millett, two members of the U.S. Court of Appeals for the District of Columbia Circuit and potential nominees for Obama to pick to replace Scalia, were seen in the line of those paying their respects along with other judges on the DC circuit.
The casket was placed on the Lincoln Catafalque, which was loaned to the court by Congress for the ceremony, and a 2007 portrait of Scalia by Nelson Shanks is on display. Supreme Court police officers served as pallbearers while Scalia's law clerks served as honorary pallbearers.
"As is the tradition, Justice Scalia's law clerks will stand vigil by his side at the Court all day tomorrow and through the night," tweeted Kannon Shanmugam, who clerked for Scalia.
Outside the court, mourners left flowers and jars of applesauce -- a nod to Scalia's dissent in the Supreme Court's 2015 decision to uphold Obamacare, in which he wrote that the majority's opinion was "pure applesauce."
Scalia's funeral service is Saturday at the Basilica of the National Shrine of the Immaculate Conception. The justice's son will also deliver Mass for his father. Vice President Joe Biden is scheduled to attend.
Other justices who have laid in repose in the Supreme Court include former Chief Justice William Rehnquist, former Justice Harry Blackmun, former Justice William J Brennan Jr., former Justice Thurgood Marshall and former Chief Justice Earl Warren.
One close family friend -- Brian Donato, 75, of Earlysville, Virginia, and the godfather of Paul Scalia -- was shaken up as he left the morning's private ceremony.
He said he studied law under Scalia at the University of Virginia, and called the justice a tough professor who'd harshly critique his logic.
Donato recalled leaving the U.S. Navy in 1967 to attend law school, and said his moving truck crashed, spilling his goods and possessions across the road. When neither the Navy, which had hired the movers, nor the moving company itself offered any financial help after the crash, he looked at the university for a lawyer to help him after that crash and found Scalia -- who won the case but wouldn't accept any legal fees.
"When I asked him what the fee was after the case, he said, 'Dinner at your house and I'm bringing my wife,'" Donato said.
He attended Thursday's wake for Scalia, saying he saw his friend "lying in his casket, and he looked like a guy who was just the warm loving guy he always was."
Students on a field trip from St. Mary's High School, an Episcopal school in Raleigh, North Carolina, were among the crowd of about 200 on hand as Scalia's casket arrived.
"It's definitely a big loss for our country he was definitely a very influential figures and I don't necessarily agree with him on everything but I have a lot of respect for him as a justice," said Emily Weatherspoon, 17.
Larry Cirignano, an anti-abortion rights activist, said that Scalia's loss will be felt on the court. His group, 40 Days for Life, has been outside of the Supreme Court every day since Ash Wednesday.
"I'm from New Jersey originally, so he's great -- and Italian-American -- so all the way around," he said of Scalia. "I was here for his swearing in. And we're sorry to see him go."
As Scalia is remembered Friday, talk is likely to also focus across the street, to the Capitol, where the question hovers over whether Senate Republicans will successfully block Obama from winning a third appointment to the High Court.