“We were put in this position of power and importance to make decisions for the people who so proudly elected us, the most important of which has long been considered to be the selection of United States Supreme Court Justices,” Trump tweeted Saturday morning. "We have this obligation, without delay!"
Later, before departing the White House for a campaign rally in North Carolina, he told reporters that he will decide on a nominee by "next week," calling his shortlist "the greatest list ever assembled."
"I think it's probably, from a legal standpoint, from a sophisticated understanding of the law, from a constitutional standpoint, I think it's the greatest list ever assembled," Trump said, adding he most likely will be choosing a woman.
"If somebody were to ask me now, I would say that a woman would be in first place, yes," he said. "The choice of a woman, I would say, would certainly be appropriate."
Multiple sources familiar with the president's thinking and that of his advisers see a shortlist of potential nominees.
The sources describe that list, as of now, as including federal appeals court judges Amy Coney Barrett, Barbara Lagoa, Allison Jones Rushing and Amul Thapar, with the sources all describing Barrett as the leading contender at this point.
The sources caution the process is still in its early stages and the president is expected to speak to those on the shortlist before making any announcement in the coming days.
When asked about Barrett Saturday afternoon, Trump said she was "very respected." He called Lagoa an "extraordinary person" and "Hispanic" and also highly respected.
Trump repeated he wanted a vote before Nov. 3.
"I would think before would be very good, but we'll be making a decision," he said. "I think the process can go very, very fast. I will be making my choice soon and when the choice is made, I will be sending it over to Mitch in the Senate and they will do what they have to do," he said, referring to Senate Majority Leader Mitch McConnell.
McConnell said Friday the Senate would vote on a Trump nominee, although he didn't specify when, and just how quickly the process will move on the Capitol Hill is still very much an open question with the election just over six weeks away.
“Americans reelected our majority in 2016 and expanded it in 2018 because we pledged to work with President Trump and support his agenda, particularly his outstanding appointments to the federal judiciary,” McConnell said in a statement Friday night.
Some Republicans seem to be answering Trump's call. Sen. Thom Tillis, a longtime Trump ally who currently is in a tough reelection slog against Democrat Cal Cunningham, made it clear he’ll support a Trump nominee.
"There is a clear choice on the future of the Supreme Court between the well-qualified and conservative jurist President Trump will nominate and I will support, and the liberal activist Joe Biden will nominate and Cal Cunningham will support, who will legislate radical, left wing policies from the bench," Tillis said in a statement.
Ginsburg's death sets the stage for a titanic political showdown that complicates an already bitter presidential election. Not even 24 hours after news broke of Ginsburg's death, the White House and Trump campaign leaned into the new political reality by urging former Vice President Joe Biden to release his list of possible Supreme Court picks as Trump did last week.
"He needs to tell voters where he stands," White House press secretary Kayleigh McEnany told Fox News Saturday morning.
"We don't know who's on his Supreme Court list. We don't know what kind of justices he would nominate. We know very squarely this president has been very transparent putting forward two lists as to exactly not just what his justices would look like but what their names be. This is paramount importance to the American voters," she said.
Trump appeared to be caught off guard Friday evening when a reporter asked him about Ginsburg's death and said that he was "saddened" to hear the news.
“She just died? Wow, I didn't know that — I just, uh, you’re telling me now for the first time,” Trump said. "“She led an amazing life. What else can you say? She was an amazing woman, whether you agreed or not, she was an amazing woman who led an amazing life. I'm, actually saddened to hear. I am saddened to hear that.”
The sense of urgency Trump expressed Saturday is in sharp contrast to how he reacted after the death of Justice Antonin Scalia four years ago while President Barack Obama was in his last year in office.
"I think that the next president should make the pick," Trump said on CNN at the time. "We don't have a very long distance to wait. Certainly, they could wait it out very easily. But I think the next president should make the pick. I would be not in favor of going forward."
NPR reported that just days before her death, Ginsburg dictated this statement to her granddaughter Clara Spera: "My most fervent wish is that I will not be replaced until a new president is installed."
ABC News' John Santucci, Katherine Faulders, Will Steakin and Trish Turner contributed to this report.