President Donald Trump said Tuesday he will announce his pick on Saturday for the crucial Supreme Court seat left open by the death of justice Ruth Bader Ginsburg, as Republicans firmed up their majority to vote on the nominee.

Democratic opponents, led by presidential candidate Joe Biden, have demanded that the Republicans back off on replacing Ginsburg -- who died last week -- until after the November 3 election.

The vacancy would be the third filled by Trump, meaning he could shift the nation's high court to the right for decades to come -- perhaps even if he loses his bid for a second term.

"I will be announcing my Supreme Court Nominee on Saturday, at the White House! Exact time TBA," Trump said.

Trump had originally indicated he would reveal his choice early this week, but delayed out of respect for the memorial services for Ginsburg taking place in the capital.

He has said he will choose a woman for the lifetime post.

On Capitol Hill, the Republicans -- who control the Senate, which votes to confirm Supreme Court nominees -- solidified their majority to ensure the candidate gets a vote.

Although two Republican senators said they believed the upper chamber of Congress should not vote on a pre-election Trump pick, the party's 53-47 majority is still just big enough to go ahead.

Four Republicans would likely have had to break ranks in order to block a vote from taking place.

But Mitt Romney, a frequent critic of Trump whom some Democrats had hoped would refuse a vote, said he would move ahead with the process.

"I intend to follow the Constitution and precedent in considering the President's nominee," Romney said in a statement.

"If the nominee reaches the Senate floor, I intend to vote based upon their qualifications."

Fellow moderate Republican Senator Cory Gardner also signaled his intent to proceed with any nomination submitted to the upper chamber of Congress.

"I have and will continue to support judicial nominees who will protect our Constitution, not legislate from the bench, and uphold the law," Gardner said.

"Should a qualified nominee who meets these criteria be put forward, I will vote to confirm."

'Abuse of power'

Democrats argue any Senate vote should be delayed until after the election has made clear who will lead the country from 2021.

They cite the example of 2016 when, under then president Barack Obama, his nominee to replace Antonin Scalia months before the election did not even get a hearing.

Republicans say that with their control of the White House and the Senate right now, they have the right to fill court seats at any time they wish.

Further muddying the waters is fear that leaving Ginsburg's seat unfilled -- reducing the court to eight justices -- raises the possibility of a 4-4 tie in the event of rulings related to election disputes.

Trump's Saturday announcement will set the clock ticking on what is likely to be a contentious, high-stakes political fight as Republicans push to get the nominee confirmed at an unusually fast pace.

Although Democrats have no way of stopping the procedure, they will seek to inflict political pain on the Republicans over what Biden has called an "abuse of power."