"I hope she gets better and I hope she serves on the Supreme Court for many, many years", Trump said.
She went to George Washington University Hospital early Thursday morning after experiencing discomfort overnight.
"I'm now 85", Ginsburg said. "I can't promise they were good jokes but they were jokes", he said.
"I wish her well. She is doing well and plans to work from home today", a U.S. Supreme Court spokesperson said in a statement Friday.
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Celebrated in popular culture as the "notorious RBG" and at age 85 the court's oldest justice, Ginsburg is a liberal stalwart who has said she will not retire as long as she feels she can do the work.
"Ginsburg has had a series of health problems", reports AP. As a result, she was forced to miss the formal investiture ceremony for new Associate Justice Brett Kavanaugh at the court that morning.
The Supreme Court's oldest justice, Ginsburg has previously survived two forms of cancer and a heart procedure to have a stent placed in her right coronary artery.
In 2012, she fell and broke two ribs, and in 2009 she was hospitalized after a negative reaction to medication.
Ginsburg was appointed in 1993 by former President Bill Clinton.