US Sen. Al Franken said Thursday that he will give up his Senate seat amid allegations of sexual harassment leveled by eight different women.

The Minnesota Democrat made the announcement in a brief speech on the Senate floor, saying that "in the coming weeks" he would resign his Senate seat.

He referred to the accusations against President Donald Trump and the Republican candidate in Alabama's special Senate seat election next week, Roy Moore.

"There is some irony that I am leaving while a man who bragged on tape about his history of sexual assault sits in the Oval Office, and a man who preyed on young girls runs for Senate with the full support of his party," Franken said.

The former comedian - who had apologized for any offense he may have given to anyone, particularly the women who claimed he had unwanted sexual contact with them, and who has offered to be investigated by the Senate Ethics Committee - is one of the most popular Democratic senators, with his name having been heard in connection with a possible presidential run in 2020.

Although convinced of his innocence, the senator used his brief Senate floor remarks on Thursday to defend himself against the accusations leveled at him, charges he has denied in some cases and tried to explain in others.

Some of the allegations against him, he said, "are simply not true. Others I remember differently."

He also made a distinction between certain of his acts before he entered the Senate in 2009 and afterward.

"Nothing I have done as a senator - nothing - has brought dishonor on this institution. And I am confident that the Ethics Committee would agree," he said.

He also said he was proud of the fact that during his time in the Senate he used his office to be a champion of women's rights, he told the lawmakers on hand to hear his remarks.

Franken's resignation announcement comes five days before Alabama's special election, where Moore has not withdrawn from the race despite being accused of sexual harassment of underage girls, a situation that did not dissuade Trump from giving his public backing to the controversial candidate.

The 66-year-old Franken has been accused of kissing and touching women without their consent in 2003 and 2010.

He announced his resignation in the same week that Democratic lawmaker John Conyers, of Michigan, announced that he will not run for re-election in 2018 after more than 50 years in Congress because of numerous requests from his party colleagues to leave office after a series of accusations of sexual abuse.

The US over the past few months has been beset by a wave of sexual harassment complaints, beginning with the scandal surrounding Hollywood film producer Harvey Weinstein and then spreading to figures in the political and other realms.