Trump disparaged reports that Ginsburg had told her granddaughter it was her wish that a replacement justice not be confirmed until the inauguration of a new president.
Trump said he thought his Democratic political foes were behind the report, including Rep. Adam Schiff, who led the House impeachment probe, House Speaker Nancy Pelosi, and Senate Democratic Leader Chuck Schumer..
"I don't know that she said that, or was that written out by Adam Schiff and Schumer and Pelosi," Trump said. "I would be more inclined to the second ... But that sounds like a Schumer deal or maybe a Pelosi or Shifty Schiff." his nickname for the California congressman.
President Trump on Saturday promised to put forth a female nominee in the coming week to fill the Supreme Court vacancy created by the death of Justice Ruth Bader Ginsburg, pushing the Republican-controlled Senate to consider the pick without delay.
WATCH: What's next for the Supreme Court? McConnell says Senate will vote on replacement
Those under close consideration for the high court include three women who are federal appeals court judges: Amy Coney Barrett, beloved among conservatives and an early favorite; Barbara Lagoa, who is Hispanic and comes from the battleground state of Florida; and Allison Jones Rushing, who clerked for Justice Clarence Thomas and for Neil Gorsuch, when the current Trump-appointed justice was an appeals court judge.
At least one man, appeals court Judge Amul Thapar, has also been under consideration. An ally of Senate Majority Leader Mitch McConnell from Kentucky, he has been screened by Trump's team for past openings and he would be the first Asian-American on the high court.
McConnell, who sets the calendar in the Senate and has made judicial appointments his priority, declared unequivocally in a statement that Trump's nominee would receive a confirmation vote. In 2016, McConnell refused to consider President Barack Obama's nominee months before the election, eventually preventing a vote on Judge Merrick Garland.
Senate Democratic leader Chuck Schumer of New York convened a conference call with Democratic senators at midday Saturday, according to a person on the private call who was not authorized to discuss it publicly and spoke on condition of anonymity. He told senators the "number one goal" must be to communicate the stakes of the confirmation vote.
Schumer also warned that if Republicans push through the nominee, "nothing is off the table" for Senate rules changes to come, the person said.
WATCH: Trump calls Ruth Bader Ginsburg 'an amazing woman' following news of her death
Ginsburg's death seemed certain to stoke enthusiasm in both political parties as the election could now be viewed as referendum on the high court's decisions, including the future of abortion rights. Democrats raised more than $71 million in the hours after Ginsburg's death, indicating her passing has already galvanized the party's base.
McConnell has launched a risky, unprecedented strategy. It could motivate conservative voters to rally behind Trump and GOP senators or it could push away moderates who prefer to see the Senate stick to norms or are fearful of a right-leaning court stripping away women's right to choose an abortion.
Typically, it takes several months to vet and hold hearings on a Supreme Court nominee, and time is short before November. Key senators may be reluctant to cast votes so close to the election. With a slim GOP majority, 53 seats in the 100-member chamber, Trump's choice could afford to lose only a few.
RELATED: President Trump, Joe Biden comment on death of Ruth Bader Ginsburg
McConnell did not specify the timing. But trying for confirmation in a lame-duck session after the Nov. 3 election, if Trump had lost to Biden or Republicans had lost the Senate, would carry further political complications.
Democrats immediately denounced McConnell's move as hypocritical, pointing out that he refused to call hearings for Garland 237 days before the 2016 election. The 2020 election is 46 days away.