The court was scheduled to hold arguments on six days over two weeks, with the session culminating April 1 with a highly anticipated case: President Donald Trump's challenge of efforts by congressional committees and a New York prosecutor to subpoena his financial records.
Also on the court's agenda is a long-running $8 billion copyright legal battle Google and Oracle, and a test of which employees of religious schools are covered by anti-discrimination laws.
"The court will examine the options for rescheduling those cases in due course in light of the developing circumstances," said a statement from spokeswoman Kathleen Arberg.
The court closed for public tours and lectures last week, although it remains open for official business
The justices will meet for their regularly schedule private conference on Friday. Arberg said some justices may participate via telephone.
Lawyers and parties in the 11 cases scheduled for the next round of hearings have been anxiously awaiting word from the court. Its chamber holds about 500 people, well above what the Centers for Disease Control said the maximum should be for public gatherings.
Spectators, lawyers, journalists and court personnel share the close quarters, and a majority of the justices are considered to be in the higher risk category for coronavirus due to their ages.
Justice Ruth Bader Ginsburg turned 87 on Sunday, and Justice Stephen Breyer is 81. Justice Clarence Thomas is 71, and Samuel Alito turns 70 on April 1. Chief Justice John Roberts and Sonia Sotomayor are 65.
As the court's news release noted, little is clear about how the postponement will affect the its work. It has one other two-week round of oral arguments scheduled to end April 29.
Generally, the court doesn't hold oral arguments after that, to concentrate on writing and issuing opinions in the cases it has heard since October. The court usually finishes its work by the end of June, but nothing would prevent the court from extending the term.
Some have urged the court to use the crisis as a chance to explore other options. The court does not allow cameras in the courtroom, nor live audio of its proceedings. Transcripts of the day's oral arguments are available on the court's website, and tapes are released at the end of the week.
The cases involving Trump raises the prospect of a landmark election-year ruling on a president's immunity from investigation while he is in office.
Manhattan District Attorney Cyrus Vance Jr. and three Democratic-led congressional committees have won lower-court decisions granting them access to a range of Trump's financial records relating to him personally, his family and his businesses.
The court in December accepted Trump's request to review the decisions.
One liberal group urged the court to make sure it continues its work.
"This postponement should not delay the high court's resolution of the critical cases currently pending before it, particularly the cases involving congressional and grand jury subpoenas of the president's financial records," said Elizabeth Wydra, president of the Constitutional Accountability Center.
"Whether it means holding videoconference and telephonic hearings as other federal courts do, or using some other method, we are confident the Supreme Court can adapt to the extraordinary circumstances in which we find ourselves and continue to do its job."
The court generally is loath to stray from its schedule. When the rest of Washington shutters for snowstorms, the court carries on. It held oral arguments in 2012 when Hurricane Sandy had closed the rest of official Washington, although it later pushed back arguments for a day.
But the court's news release noted that "postponement of argument sessions in light of public health concerns is not unprecedented." Besides the 1918 recess, the court "also shortened its argument calendars in August 1793 and August 1798 in response to yellow fever outbreaks.
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