A second Senate Republican has voiced objections to US President Donald Trump's plan for a quick vote on a replacement to Supreme Court liberal Justice Ruth Bader Ginsburg, who died on Friday.
Such an appointment by the president, if approved by the Senate, would cement a 6-3 conservative majority that could influence American law and life for decades.
Democratic presidential candidate Joe Biden said that if he wins the 3 November election, he should have the chance to nominate the next Supreme Court justice.
The former vice president rejected the idea of releasing the names of potential nominees, saying that doing so, as Mr Trump did, could improperly influence those candidates' decisions in their current court roles as well as subject them to "unrelenting political attacks".
Senator Lisa Murkowski of Alaska said she did not support Mr Trump's plan to move fast on filling the seat, becoming the second of the 53 Republicans in the 100-seat chamber to object publicly following Judge Ginsburg's death.
On Saturday, Republican Senator Susan Collins of Maine said the presidential election winner should pick the nominee. She is locked in a tight re-election battle, while Ms Murkowski's current term extends two more years.
Senator Lamar Alexander, another moderate Republican, said in a statement he did not object to a vote, adding: "No one should be surprised that a Republican Senate majority would vote on a Republican president's Supreme Court nomination, even during a presidential election year."
Democrats noted that in 2016 Republican Senate Majority Leader Mitch McConnell blocked a vote on a Democratic appointee on the grounds that the vacancy should be filled by the next president.
Senate Democratic leader Chuck Schumer did not rule out that his party might move in future to end the filibuster, a procedural tactic under which the support of 60 members is required to move to a vote on legislation, if the Republicans went ahead with the nomination.
"We first have to win the majority... But if we win the majority, everything is on the table," he said.
Mr Schumer and US Representative Alexandria Ocasio-Cortez of New York told a joint news conference that putting another conservative on the court would put at risk healthcare and women's and LGBTQ rights.
A majority of Americans, some 62% including many Republicans, told a Reuters/Ipsos poll that they thought the winner of the November election should get to nominate a justice to fill the vacancy.
Justice Antonin Scalia, a close friend of Ginsburg's, died in February 2016, but Mr McConnell blocked a vote on Democratic President Barack Obama's Supreme Court nominee, Merrick Garland.
Mr Trump said on Saturday he would make his nomination this week and named Amy Coney Barrett of the Chicago-based 7th US Circuit Court of Appeals and Barbara Lagoa of the Atlanta-based 11th Circuit as possible candidates to fill the vacancy created by Judge Ginsburg, a revered figure among liberals.
Mr Biden has also said he will pick an African-American female nominee.