Kavanaugh's confirmation puts him on the nation's highest tribunal - but at the bottom of its ritualistic pecking order.
But when asked on "Fox News Sunday" if that would apply in 2020, McConnell said: "We'll see if there is a vacancy".
It was the closest roll call to confirm a justice since 1881, when Stanley Matthews was approved by 24-23, according to Senate records.
When Flake cast his vote in favor of Kavanaugh, one protester shouted, "You're a coward Flake, a total coward!" Retiring Republican Rep. Lynn Jenkins holds the seat, and Democrats hope to flip it.
"It's a good day for America and an important day for the Senate", McConnell said at a news conference following Kavanaugh's confirmation vote on Saturday.
Susan Rice, who was President Barack Obama's national security adviser, said Sunday she'll decide after next month's midterm elections whether to run for the Senate from ME in 2020 and try to unseat Republican Sen. Joe Manchin voted against Kavanaugh while every Republican - except Sen.
She also said after an event in Norridgewock on Sunday that the response of Mainers has been "overwhelmingly positive:" "Many people have thanked me for my vote and have said that they were very pleased that I did the right thing".
Ms Murkowski opted instead to simply mark herself as "present", leaving the final vote 50-48.
Republicans now hold a 51-49 majority in the Senate, with several seats up for grabs in November.
Within minutes, dozens of political and advocacy groups blasted out emailed reactions.
"It's energized our base going into the election in a way we had not been able to figure out how to do prior to this", McConnell said. "Women will not forget this".
The final vote Saturday capped a bitter confirmation process that included a heated Capitol Hill hearing on the abuse allegations Palo Alto University professor Christine Blasey Ford leveled against him in September. The court's two oldest justices are Democratic appointees: Ruth Bader Ginsburg is 85 and Stephen Breyer is 80.
Kavanaugh's nomination sparked protest across the Capitol, which continued Saturday.
Though the fight to confirm Trump's pick is now official over, the impact of Kavanaugh's confirmation will have a lasting effect.
During his 12 years on the U.S. Court of Appeals for the D.C. Circuit, a majority of the clerks he hired were women, which he said should be an indicator of his views about women in the workplace. Hundreds of other demonstrators watched from behind barricades.
Because, make no mistake, in an election cycle that may well turn out to be the year of the woman, the Republican Party's treatment of Christine Blasey Ford and other Kavanaugh accusers as well the conduct of party leaders like Chuck Grassely have made amply clear that the GOP is the party of men. But she also said the Federal Bureau of Investigation had found no corroborating evidence from witnesses whose names Ford had provided.
She acknowledged the anguish of the protesters who interrupted the historic Senate vote, telling reporters afterward that "I was closing my eyes and praying".
The economy, which Mr Trump claims has been spurred by aggressive tax cuts and cuts to regulation, is now in its best shape for years.
"Democrats have been trying to destroy Judge Brett Kavanaugh since the very first second he was announced", Trump declared as he rallied voters in Minnesota on Thursday night. For her, it comes down to believing that Kavanaugh will uphold Roe v. Wade. But Trump went after her anyway, mocking her testimony and gaps in her memory as a rally crowd laughed and cheered.
Ford said she was "100 percent" certain that Kavanaugh was her attacker, while the judge steadfastly denied her allegations.
United States president Donald Trump had nominated Kavanaugh on July 9, 2018, as a replacement of Associate Justice Anthony Kennedy.
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