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Ms Ginsburg was an iconic leader of women's rights in America and became a prominent feminist figurehead.
Ginsburg died at her home in Washington of complications from metastatic pancreatic cancer, surrounded by her family, the court said.
Ginsburg's death marked the loss of a liberal justice on the court.
In a statement, Chief Justice John Roberts said: "Our Nation has lost a jurist of historic stature".
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Ginsburg was nominated to the Supreme Court in 1993 by President Bill Clinton, the second woman to serve on the United State's highest court.
The directors of the documentary "RBG", Betsy West and Julie Cohen, said in a statement, "Like so many Americans, we are crushed by the death of Justice Ruth Bader Ginsburg". Lisa Murkowski, R-Alaska, told Alaska Public Media on Friday, as it was being discussed as a hypothetical scenario, that she wouldn't support confirming a new justice until after the presidential election.
She was appointed a Judge of the United States Court of Appeals for the District of Columbia Circuit in 1980.
Her departure could dramatically alter the ideological balance of the court, which now has a 5-4 conservative majority, by moving it further to the right.
On Friday night, Senate Majority Leader Mitch McConnell has said Mr Trump's nomination for Ms Ginsburg's replacement will receive a vote on the Senate floor.
Trump says United Nations must 'hold China accountable' for Covid-19
He referred to the Covid-19 virus as the " China virus" - something he's repeatedly done before. "The world is at a crossroads". No country should "be allowed to do whatever it likes and be the hegemon, bully or boss of the world ", he said.
Minority Leader Chuck Schumer said in a statement that American's should have their vote in the U.S. election before the vacancy is filled.
The big question is thus: Can a Supreme Court justice be replaced during an election year-like the one we're in?
Our Democratic colleagues continually talk about the so-called 'Thurmond Rule, ' under which the Senate supposedly stops confirming judges in a presidential election year.This seeming obsession with this rule that doesn't exist is just an excuse for our colleagues to run out the clock on qualified nominees who are waiting to fill badly needed vacancies.Her death was announced by the Supreme Court.
Congressional candidate Ammar Campa-Najjar said of the Jewish justice: "It's with a heavy heart we say goodbye to her tonight, on the eve of Rosh Hashanah". I didn't know that.
"Her life has inspired generations to always pursue justice for all", Gomez tweeted.
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"What else can you say?" Without her leadership and conviction, the world would be a different place for women, people of color, and other marginalized communities. "I am sad to hear that". "And that is to honor her last words that she not be replaced until a new president is installed".