Sports broadcaster and former model Leeann Tweeden also accused Franken, a former comedian once tipped as a possible White House candidate, of kissing her without her consent.

Franken has apologised and said he does not remember that second incident in the same way, but he now faces a Senate ethics investigation that could see him fined, stripped of committee posts or even expelled.

Tweeden told ABC’s Good Morning America on Friday that she decided to come forward because she hopes to encourage other victims of sexual harassment and assault to tell their stories in “real time”. Tweeden says she did not speak out at the time of the incident because she felt complaining would hurt her career.

When asked if Franken should step down, Tweeden said: “That’s not my call. I did not do this to have him step down … I think that’s for the people of Minnesota to decide.”

Until now, the White House had tried to distance Trump from a rolling series of scandals that have reverberated from Hollywood to the halls of Congress.

As the storm of allegations has swirled, Trump – who himself has faced more than a dozen allegations of sexual misconduct – had largely avoided comment.

For days he refused to call on Republican senate hopeful Roy Moore to bow out of the race after being accused of sexual advances toward several teenagers.

But the US president appeared unwilling to pass up an opportunity to attack a Democrat who has been hyper critical of his conduct as president.

“And to think that just last week he was lecturing anyone who would listen about sexual harassment and respect for women,” Trump said in a second tweet.

Franken is also on the judiciary committee, which is among those looking into Russia’s role in the 2016 election.

As president and as celebrity, Trump has frequently injected himself into developments to which he has little connection – from the shooting of Harambe the gorilla to NFL anthem protests.

But this intervention may pose more political risk for the 71-year-old.

In response to his latest foray, Trump critics immediately zeroed in on allegations against the president and his infamous remarks in which he boasted about grabbing women by the genitals.

Earlier on Thursday, the White House said Trump believes the allegations against Moore were “very troubling and should be taken seriously.”

Several women stepped forward to accuse the would-be senator Moore of decades-old impropriety, including a woman who said he initiated a sexual encounter when she was 14.

Watch: radio host accepts senator’s apology

But White House press secretary Sarah Sanders said Trump’s accusers should not be believed in the same way.

“I think the president has certainly a lot more insight into what he personally did or did not do, and he spoke out about that directly during the campaign,” she said.

Moore, now 70, has also denied any wrongdoing and said he will contest the December 12 poll.

The allegations against Moore are politically charged for the White House. They have heightened ideological splits in the Republican Party and could help decide who controls the Senate.

Republicans control 54 of 100 seats in the Senate, but if Democrats win in Alabama, victories in tight races in Arizona and Nevada and an upset elsewhere would put them in charge.

Privately some Republicans admit the race may now be lost, with the Republican vote split between Moore’s diehard supporters and so called “write-in” candidates who are not on the ballot.

Additional reporting by Associated Press