Sen. Tom Cotton (R-Ark.) said the Senate will move forward in confirming a new Supreme Court justice after Justice Ruth Bader Ginsburg died on Friday.
"The Senate will exercise our constitutional duty," Cotton said, adding that the Senate will have nomination hearings.
"We will move forward without delay," the Arkansas senator said.
Cotton said that it's not clear if the vote would happen before the November election, but that it is a possibility.
"There will be a vote. There have been some cases, like Justice Ginsburg herself" when the confirmation process "took less than 44 days," he added. "There have been other cases [in] which it took longer, so it's too soon to say right now."
Senate Majority Leader Mitch McConnell (R-Ky.), following Ginsburg's passing, said that he will try in earnest to nominate a Supreme Court justice as soon as possible. "President Trump's nominee will receive a vote on the floor of the United States Senate," he said.
Meanwhile, President Donald Trump told a crowd Saturday in North Carolina that he'll nominate a woman judge.
"I will be putting forth a nominee next week. It will be a woman," he said in Fayetteville. "I think it should be a woman because I actually like women much more than men."
There is speculation that Trump will look to nominate Judge Amy Coney Barrett or Judge Barbara Lagoa. He praised the two in the rally.
Trump, who already selected two Supreme Court justices during his presidency, said that a nomination would give conservatives a decisive advantage in key decisions.
"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. We have this obligation, without delay!" he wrote on Twitter Saturday.
Ginsburg, a left-wing icon and standard-bearer for feminism, died of metastatic pancreatic cancer in her home in Washington, surrounded by her family. She was the second woman to serve on the Supreme Court. Former Supreme Court Justice Sandra Day O'Connor was the first.
Senate Minority Leader Chuck Schumer (D-N.Y.), wrote a tweet, "American people should have a voice in the selection of their next Supreme Court Justice. Therefore, this vacancy should not be filled until we have a new president."
Meanwhile, Democratic nominee Joe Biden said the Supreme Court justice should be selected by whoever wins the presidency in November.
"There is no doubt—let me be clear—that the voters should pick the president and the president should pick the justice for the Senate to consider," he told reporters over the weekend.