"We have an obligation to do what's right and act as quickly as possible." the president said. "We should act quickly because we're going to have probably election things involved here, you know, because of the fake ballots that they'll be sending out which is a terrible. ... We don't want to have a tie, no, we don't. And we want to have nine justices."

GOP Sen. Lindsey Graham of South Carolina, the chairman of the Judiciary Committee and who would oversee confirmation hearings, said in a letter to Democratic members of the panel on Monday that he will move forward with Trump's nominee, despite his past public assurances that he would not during an election year. Graham, in his letter, cited what he saw as unfair treatment of Trump's other nominees, such as Justice Brett Kavanaugh.

"Because our Senate majority committed to confirming President Trump’s excellent judicial nominees — and particularly because we committed to supporting his Supreme Court nominees — the American people expanded the Republican majority in 2018. We should honor that mandate," he said in the letter.

"I therefore think it is important that we proceed expeditiously to process any nomination made by President Trump to fill this vacancy. I am certain if the shoe were on the other foot, you would do the same."

GOP Sen. John Cornyn of Texas told reporters on Monday that he has doubts that a nominee could be nominated and confirmed before Election Day.

"The ones that have been done more quickly have typically been done with a lot more cooperation," he said. "I think I'm not expecting much cooperation from the Democrats."

Reacting to the decision by two Republican senators — Susan Collins of Maine and Lisa Murkowski of Alaska — to oppose holding a confirmation vote before the election, Trump said that Collins is "very badly hurt by her statement" in her re-election race. He also suggested that Murkowski's stance would haunt her in a future race as well.

Asked about Ginsburg's dying wish, in which she reportedly said she didn't want to be replaced until a new president was in office, Trump said, without evidence, "I don't know that she said that, or was that written out by Adam Schiff and Schumer and Pelosi? I would be more inclined to the second, OK, you know. It came out of the wind, it sounds so beautiful. But that sounds like a Schumer deal, or maybe a Pelosi or shifty Schiff. So that came out of the wind."

Democratic Sen. Joe Manchin of West Virginia, who would be a key vote, said in a Monday statement that he also opposes nominating and voting on a judicial nominee before Election Day.

"For Mitch McConnell and my Republican colleagues to rush through this process after refusing to even meet with Judge Merrick Garland in 2016 is hypocrisy in its highest form," he said. "I implore every Senator, regardless of party, to honor their responsibility to act in a manner that brings this country together rather than feed a cycle of endless political division.”

Just days before she died, Ginsburg dictated a statement to her granddaughter Clara Spera that said, "My most fervent wish is that I will not be replaced until a new president is installed," NPR reported.

Geoff Bennett, Pete Williams and Peter Alexander contributed.