"The Court will examine the options for rescheduling those cases in due course in light of the developing circumstances," spokeswoman Kathy Arberg said in a statement.
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The delay of cases is believed to be the most significant disruption to the court's business since the 1918 Spanish flu epidemic when several arguments were postponed for roughly a month, according to court records. The court also shortened its August sessions in 1793 and 1798 due to yellow fever outbreaks, the court said.
The justices, many of whom are among the most at-risk for COVID-19 given their age and underlying health conditions, remain in good health and continue to work on court business from home or their private chambers, Arberg told ABC News.
Six justices are 65 or older. The oldest, Justice Ruth Bader Ginsburg, turned 87 on Sunday.
The postponed cases, which had been scheduled for arguments March 23-25 and March 30-April 1, include appeals from President Donald Trump in three separate lawsuits seeking access to his personal financial records, including tax returns, personal checks and credit card transactions.
Other delayed cases include a high-profile military rape case that will decide whether a five-year statute of limitations should stand for certain prosecutions. The court was also set to hear a First Amendment case involving alleged discrimination by a religious employer and a Fourth Amendment challenge in a police shooting case.
It's unclear when the cases will be rescheduled or if the court will need to extend its term, which concludes at the end of June.
The justices will hold a regularly scheduled private conference on Friday to discuss pending cases and petitions before the court, with at least some justices joining by telephone, Arberg said in the statement.
Postponement of public sessions at the Supreme Court reflects Center for Disease Control and Prevention guidelines to avoid large gatherings and close personal interaction during the pandemic, Arberg said. The court's chamber holds roughly 500 people. On the bench, the justices sit nearly shoulder to shoulder while attorneys arguing cases stand just several feet away.
Last week, the court closed its building to the general public even as it said official business would continue. Employees are being told to telework as much as possible.
Opinions in several high profile cases could still be handed down in the coming weeks, the court said, including rulings on Trump's cancellation of DACA for young undocumented immigrants and on employment discrimination against LGBT Americans. Both were argued earlier this year with decisions expected any day.