President Trump on Monday reiterated during a campaign rally that he will nominate a woman to fill the empty seat on the Supreme Court that has been vacated following the death of Justice Ruth Bader Ginsburg.

Speaking to a raucous crowd near Dayton, Ohio, Trump said appointing Supreme Court justices is the most important job a president has and boosted that by the end of his first term in office he will have appointed 300 federal judges.

“This is the single most important thing a president does,” Trump said. “At the end of my first term, we will have appointed 300 federal judges.”

Trump also polled the crowd at his rally as to whether he should nominate a man or a woman.

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“Who would like to see a woman justice of the Supreme Court?” he asked. “Who would like to see a male justice?

“It’ll be a woman,” Trump said, adding that the White House was in the process of vetting potential nominees.

Shortly before Trump took the stage in Ohio, Fox News learned that he had earlier met with Judge Amy Coney Barrett, who sources say is the potential frontrunner to fill the vacant Supreme Court seat.

Although Trump recently released a lengthy list of potential nominees, he appeared to narrow those down over the weekend when he said he wanted a woman to fill the spot.

On Monday, Trump said he had narrowed his choices down to five. While speaking with reporters, he specifically addressed potentially nominating Barbara Lagoa, a Cuban-American who serves on the 11th U.S. Circuit Court of Appeals. “I may. She is highly thought of,” he said when asked about her.

The president told "Fox & Friends" he intended on waiting until services ended for the late justice. “I think it will be on Friday or Saturday and we want to pay respect, it looks like we will have services on Thursday or Friday, as I understand it, and I think we should, with all due respect for Justice Ginsburg, wait for services to be over," he said.

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The death of Ginsburg last Friday at the age of 87, along with speculation over Trump’s potential pick, has intensified partisan fighting in Washington.

Democrats have made a moral argument to their Republican colleagues to resist filling the seat until the next president is inaugurated, arguing that senators should follow the precedent that McConnell set in 2016.

Senate Majority Leader Mitch McConnell, however, says the current situation is different because the Senate and the presidency are held by the same party, which was not the case when a vacancy opened under Obama in 2016. Democrats say this reasoning is laughable and claim the vacancy should be kept open until after the inauguration.

Both Trump and McConnell have also made a concerted effort to fill vacant federal court seats with their picks – something Trump was heard bragging about during a recorded interview with Washington Post associate editor Bob Woodward.

Trump ragged on his predecessor, President Barack Obama, for leaving more than 100 vacancies in the federal courts – calling them “golden nuggets” during an interview with Woodward in May that was released publically on Sunday.

Most of the vacancies on the federal bench were caused by McConnell’s efforts in the Republican-controlled Senate to block or delay Obama appointees – marking the slowest confirmation rate for judges in more than 60 years.

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The most prominent move by McConnell to thwart an Obama appointee was in 2016 when he declined to act on Obama’s nomination of Merrick Garland to succeed the late Justice Antonin Scalia in an election year.

“You know what Mitch’s biggest thing is in the whole world? His judges,” Trump told Woodward. “He will absolutely ask me, ‘Please, let’s get the judge approved instead of 10 ambassadors.'”

Monday is just the beginning of the battle over Ginsburg's seat. President Trump said that he hoped to have a vote on a nominee before the presidential election on Nov. 3, which would represent a very accelerated timeline for how long Supreme Court confirmations have taken in recent years.

Fox News’ Sam Dorman contributed to this report.