President Donald Trump said Saturday that he plans to nominate a woman to replace Justice Ruth Bader Ginsburg on the U.S. Supreme Court.

Trump, who made the commitment at a rally in Fayetteville, North Carolina, said he could announce a nominee as soon as next week.

“It will be a woman,” Trump told a cheering crowd. “A very talented, very brilliant woman.”

Trump’s remarks came one day after the death of Ginsburg, a pioneering jurist on gender equity issues who served on the court for more than 27 years. Trump, a Republican, is expected to pick a nominee who could solidify a conservative court for years. Ginsburg’s death is expected to become another flashpoint to a volatile presidential election year that is happening amid a global pandemic.

At the rally, Trump implied his decision on whether to select a woman to the nation’s high court could hinge on the crowd through a public poll at the event. When prompted by the president, an enthusiastic crowd cheered more loudly in support of a woman nominee versus a man.

At one point, Trump added: “I think it should be a woman, because I actually like women much more than I like men, I have to say … I do, I like women more.”

Rally attendees chanted: “Fill that seat!”

Hours earlier on Saturday, Trump made his first public reference to the possibility of nominating a woman.

“I could see most likely it would be a woman,” Trump told reporters before boarding a plane to North Carolina. “Yeah, I think I could say that it would be a woman, I would. If somebody were to ask me now, I would say that a woman would be in first place. Yes, the choice of a woman I would say would certainly be appropriate.”

Trump tweeted on Saturday morning that he had an “obligation, without delay” to select a replacement after it was made public that Ginsburg died Friday following complications from pancreatic cancer.

Trump also released a statement of admiration for Ginsburg. At the rally, he called her “an inspiration to a tremendous number of people.”

In the days before her death, Ginsburg requested that she not be replaced “until a new president is installed.”

There have been only four women who have served on the U.S. Supreme Court: Ginsburg and Justices Sandra Day O’Connor, Sonia Sotomayor and Elena Kagan.

A shortlist of potential nominees, released by the White House, has several women on it. It includes Amy Coney Barrett, a judge on the U.S. Court of Appeals for the 7th Circuit. When asked about Barrett on Saturday, Trump said, “Well, she’s very highly respected, I can say that.”

Trump was also asked about Barbara Lagoa, a judge on the U.S. Court of Appeals for the 11th Circuit. “She’s an extraordinary person, I’ve heard incredible things about her. I don’t know her. She’s Hispanic and highly respected. Miami. Highly respected.”

Senate Majority Leader Mitch McConnell has said he plans to bring a vote to the Senate floor on a Trump nominee, but it’s unclear for now whether all Senate Republicans will support it. On Saturday, U.S. Sen. Susan Collins of Maine said the Senate should wait on any Supreme Court vote until after the election.

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“In fairness to the American people, who will either be re-electing the president or selecting a new one, the decision on a lifetime appointment to the Supreme Court should be made by the president who is elected on Nov. 3,” she said in a statement.

When asked about Collins’ statement, Trump told reporters: “Well, I totally disagree with her. We have an obligation. We won, and we have an obligation as the winners to pick who we want. That’s not the next president. Hopefully I’ll be the next president. But we’re here now. Right now, we’re here, and we have an obligation to the voters, all of the people, the millions of people that put us here, in the form of a victory, we have an obligation to them, to all of those voters. And it’s a very simple thing, so I would disagree.”

Democratic presidential candidate Joe Biden has said he would nominate a Black woman to the Supreme Court if elected. Progressive judicial advocacy groups have launched a campaign, complete with a shortlist of potential picks, for him to make good on his promise.