In a speech at the National Constitution Center in Philadelphia, Biden, the Democratic presidential nominee, accused Trump and Senate Majority Leader Mitch McConnell, R-Ky., of trying to engage in "constitutional abuse" following Justice Ruth Bader Ginsburg's death Friday.
"To jam this nomination through the Senate is just an exercise in raw political power," Biden said. "I don't believe the people of this nation will stand for it."
Noting that voters have already begun casting ballots in some states, Biden said, "Their voice should be heard."
"I believe voters are going to make it clear they will not stand for this abuse of power," he said. "Constitutional abuse."
Biden said that should Trump submit a nominee, the Senate should not act until the election is resolved.
"If Donald Trump wins the election — then the Senate should move on his selection and weigh that nominee fairly," Biden said. "But if I win the election, President Trump's nomination should be withdrawn."
He called on Senate Republicans to help "de-escalate" tensions and to follow their "conscience," saying they should "cool the flames that have been engulfing our country."
"I'm speaking to those Republicans out there, Senate Republicans, who know deep down what is right for the country and consistent with the Constitution," he said. "Not just what's best for their party."
While Biden said he would not release a list of potential nominees he would put forward, he again hinted, like Trump, that his nominee would be a Black woman. He said, however, that by releasing a list of potential picks, he could give the appearance of improperly influencing their decision-making while exposing them to political attacks.
Biden said he would make his Supreme Court choice "based on what prior presidents have done," and he pledged to consult with both Democratic and Republican senators.