Trump has repeatedly ignored questions on Moore since returning from his lengthy trip to Asia. "Me too!" he added of Moore.
The revelations about sexual misconduct by Franken are among the latest in a wave of allegations against men in politics, entertainment and media, including at NPR.
Trump also accused Franken of hypocrisy, saying "just last week he was lecturing anyone who would listen about sexual harassment and respect for women". Trump was caught on tape in conversation with Access Hollywood boasting in graphic detail of sexually harassing women. "It's fake. It's made-up stuff".
The broadcaster and also a former model, Ms Leeann Tweeden, also accused Mr Franken, a former comedian, of kissing her without her consent.
Mocking Franken's name in a misspelling, the president wrote: "The Al Frankenstien picture is really bad, speaks a thousand words. Where do his hands go in pictures 2, 3, 4, 5 & 6 while she sleeps?.", Mr Trump tweeted.
Franken was then a radio talk show host, comedy writer, and author, and not yet a senator, but he issued an apology and called for an ethics investigation of the incident. And the very credible accusations against him have not been taken seriously. Two women have come forward by name accusing Moore of initiating sexual contact with them when they were 14 and 16, respectively.
Privately some Republicans admit the race may now be lost, with the Republican vote split between Moore's die-hard supporters and so-called "write-in" candidates who are not on the ballot. "The ALGOP Steering Committee supports Judge Roy Moore as our nominee and trusts the voters as they make the ultimate decision in this crucial race", the party said in a statement. Moore, running in a special election for U.S. Senate, is backed by Steve Bannon, Trump's former chief strategist. Trump is aware that any discussion about sexual harassment will eventually focus on him.
But Trump's broadsides at Franken served as an open invitation for critics to revisit his own history of alleged sexual misconduct.
Hillary, 70, the former Democratic presidential nominee who a year ago lost the White House race to Trump, 71, said that Democratic Senator Al Franken has apologised for his reported sexual misconduct and his willingness for a probe "is the kind of accountability I'm talking about".
In yet another twist in the sexual abuse saga embroiling the USA, former United States president George H.W. Bush is facing new allegations from a MI woman who said he touched her inappropriately while he was in office at an event in April 1992, CNN reported on Thursday.
"Sen. Franken has admitted wrongdoing and the president hasn't; that's a very clear distinction", Sanders said Friday when asked why Franken's single accuser should be believed and Trump's multiple accusers should not.
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