McConnell said he "generally" declines reporters' requests for him to critique "on a daily basis" the president's broadsides of political opponents and the Federal Bureau of Investigation, along with Trump's most incendiary comments about women, immigrants and other groups of Americans.
According to the Associated Press, the lifting of the ban "is something of a reward to Iowa Sen".
Many analysts predict Democrats will be able to take control of the House of Representatives, but it is far from clear if they can also capture the Senate.
The whole Kavanaugh hearing has been deeply disappointing, but at least his name will keep the discussion of sexual assault alive.
"If confirmed, I'll be the first justice in the history of the Supreme Court to have a group of all-women law clerks", he said. Kavanaugh emphatically denied the allegations.
The confirmation gave the Republican president a major political victory ahead of crucial November 6 congressional elections, with Mr Trump's second lifetime selection for the nation's highest judicial body. It's hard to recruit senators of either gender for the committee, he said. Two other women also accused him of sexual misconduct. He says "the controversy ironically produced an adrenaline shot" among Republicans.
The US Senate voted 50-48 on Saturday to confirm him, with just one Democrat supporting him.
The Alaska Republican Party is considering how it might reprimand Murkowski for her vote, but "leader" McConnell said Wednesday that there is no point in challenging Murkowski because "nobody's going to beat her". Mr Trump has begun an intensive campaign tour created to make the midterms a referendum on his presidency in the hope of maintaining swing seats.
As for the accusations against Kavanaugh, he said he found Christine Blasey Ford's account of her sexual assault "convincing" but noted that there had been no corroboration. He then did an impression of her denying that she leaked the warning to reporters.
Before hearing arguments on Tuesday, the justices turned aside appeals of a 2017 ruling authored by Kavanaugh on the lower court that struck down a 2015 environmental rule imposed under former President Barack Obama regulating a potent greenhouse gas linked to climate change.
McConnell said he doesn't agree and pointed to the fact that Murkowski had won re-election as a write-in candidate in 2010. And second, Donald Trump, isn't he the guy who has everyone chanting "lock her up" 'lock her up?' Oh boy!
"Thank you for USMCA and Mr. President thank you for the year-round E15, our farmers thank you, our Iowans thank you", Reynolds told the crowd during her remarks. Kavanaugh, in contrast, is expected to be a more decidedly conservative vote, tilting the court right for decades and leaving Roberts as the justice closest to the ideological middle.
Though Wake did not provide specific details about the uptick in sexual assault reports, she said Ford's testimony showed how hard it can be to report sexual misconduct.