Ginsburg, died on Friday, just weeks before the presidential election.
Trump’s Democratic rival, Joe Biden, insists the decision on her replacement should wait until after the vote.
The ideological balance of the nine-member court is crucial to its rulings on the most important issues in US law.
But President Trump has vowed to swear in Ginsburg’s successor without delay, a move that has infuriated Democrats, who fear Republicans will vote to lock in a decades-long conservative majority on the country’s highest court.
