KNOXVILLE, Tenn. — Phil Bredesen, the Democratic nominee in a competitive race for the U.S. Senate here, told reporters that he would not block future nominees for the Supreme Court if his party held the majority next year.

“At this point, the chances of my party of being in the majority in the Senate are minuscule,” Bredesen said after his final debate with Rep. Marsha Blackburn (R-Tenn.), the Republican nominee. “I really believe you’ve got to reach beyond party on these nominations, as we did with Ginsburg, as we did with Scalia, who got 90-plus votes. I would want to see any nominee from any president brought forward for a vote.”

Since the confirmation of Justice Brett M. Kavanaugh last week, Republicans who had refused to consider President Barack Obama’s final Supreme Court nominee have taken different positions on whether they would take up a nomination in 2020. Senate Majority Leader Mitch McConnell, who argued in 2016 that there was precedent for holding a Supreme Court seat open during an election year, has since said that the key factor was which party held control of the Senate.

“The tradition going back to the 1880s has been if a vacancy occurs in a presidential election year, and there is a different party in control of the Senate than the presidency, it is not filled,” McConnell said on Monday.

But Sen. Charles E. Grassley (R-Iowa), the chairman of the Senate Judiciary Committee who ensured that Obama nominee Merrick Garland never got a hearing in the Senate, has taken a different position on a hypothetical 2020 opening on the court.

"If I’m chairman, they won’t take it up,” Grassley said on Fox News this week, “because I pledged that in 2016.”

Bredesen, who was Tennessee’s governor from 2003 to 2011, is the only Democrat seeking an open Senate seat who has said he would have supported Kavanaugh’s nomination; Sen. Joe Manchin III (D-W.Va.) was the only Democrat who actually did so. In Wednesday night’s debate, Bredesen said that the charges of past attempts of sexual assault, leveled against Kavanaugh, were worthy of investigation, but not a reason to reject his confirmation.

“I did not think those allegations rose to the level of disqualification from the Supreme Court,” Bredesen said.

Blackburn, who had consistently supported Kavanaugh’s nomination, accused Bredesen of taking too long to announce his position because he preferred more liberal judges.

The debate itself focused more on the charges against Kavanaugh than on the ideological differences between judicial nominees. Asked after the debate about a Trump administration-backed lawsuit that would overturn the Affordable Care Act, by arguing that Congress had rendered it unconstitutional by eliminating a penalty for refusing to buy insurance, Blackburn said the insurance mandate had been terrible for Tennessee, and that a Republican Congress would likely dismantle parts of the law.

“I think that whether it is the lawsuit, or an action by Congress . . . I think you will see further action by Congress,” Blackburn said.