U.S. President Donald Trump, pushing back against women accusing him of sexual misconduct, insisted Tuesday he's the target of "false accusations and fabricated stories of women who I don't know and/or have never met."

Trump lashed out on Twitter a day after three women who previously accused him of sexual harassment shared their stories on NBC's Megyn Kelly Today.

Jessica Leeds, Samantha Holvey and Rachel Crooks on Monday also urged Congress to investigate Trump's behaviour.

Trump says Democrats "have been unable to show any collusion with Russia" and now are "moving on" to these allegations. He adds: "FAKE NEWS!"

He also attacked Sen. Kirsten Gillibrand, a New York Democrat who said Monday that Trump should resign because there were credible accusations against him. Barring that, she said, "Congress should investigate the multiple sexual harassment and assault allegations against him."

Trump tweeted on Tuesday that Gillibrand is a "total flunky for Chuck Schumer," the Senate Democratic leader. He said Gillibrand, "who would come to my office 'begging' for campaign contributions not so long ago (and would do anything for them), is now in the ring fighting against Trump."

The New York Democrat tweeted: "You cannot silence me or the millions of women who have gotten off the sidelines to speak out about the unfitness and shame you have brought to the Oval Office."

Gillibrand, whose name has been floated as a possible Democratic presidential candidate in 2020, said she would not back down.

"It was a sexist smear attempting to silence my voice, and I will not be silenced on this issue," she told reporters at a news conference.

Trump did not answer a reporter's question at a White House event later on Tuesday when asked what he meant by the tweet.

In the wake of accusations of sexual misconduct and harassment directed at powerful men in the media, Hollywood and corporate America, Gillibrand has been among those leading the push for more accountability on Capitol Hill, regardless of party affiliation.

As a result of the climate of heightened awareness, Democratic congressman John Conyers and Senator Al Franken will be leaving office in the wake of allegations of improper conduct toward women, as is Republican congressman Trent Franks.

Republican congressman Blake Farenthold of Texas, who hasn't stepped down despite a confirmed payout of $84,000 US to settle a sexual harassment lawsuit, will be subject to a House of Representatives' ethics committee hearings.

In addition, several Democratic congresswomen held a news conference on Tuesday, following up on a letter released to the public the previous evening in which they called on the House committee on oversight and government reform to investigate the Trump allegations.

"Regardless of the victim or alleged perpetrator, every voice deserves to be heard and justice demands transparency, accountability and respect of due process," read the statement signed by 59 Democratic women in Congress.

Several Democrats also took Trump to task for the wording and suggestiveness of Tuesday's tweet.

Rep. Eric Swalwell, a California Democrat, assessed Trump's tweet about Gillibrand on CNN, saying: "That was an ugly and suggestive tweet, and we all know what he was trying to say there, and it is beneath the office of the presidency."

Standing up for Gillibrand, frequent Trump foil Sen. Elizabeth Warren, a Massachusetts Democrat, tweeted to the president: "Are you really trying to bully, intimidate and slut-shame (at)SenGillibrand? Do you know who you're picking a fight with? Good luck with that, (at)realDonaldTrump. Nevertheless, (hash)shepersisted."

The phrase "she persisted" went viral earlier this year after Senate majority leader Mitch McConnell silenced Warren as she tried to read a letter from Coretta Scott King about then attorney general nominee Jeff Sessions.

For his part, Schumer told reporters, "That tweet was nasty, unbecoming of a president."

Trump donated $4,800 to Gillibrand's Senate campaign in 2010, according to federal campaign finance records.

White House press secretary Sarah Huckabee Sanders denied Tuesday the assertion that the tweet was sexist, indicating that Trump's language has been similar when he has criticized both male and female politicians of corruption.

"I think only if your mind is in the gutter, would you read it that way," she said.

Accusers return to spotlight

On Monday, the three women — Jessica Leeds, Samantha Holvey and Rachel Crooks — urged Congress to investigate Trump's behaviour.

Sanders that same day pledged to provide a list of eyewitnesses whose accounts exonerated the president.

Nearly 24 hours later, the White House sent to The Associated Press a rebuttal of just two of the alleged accounts, one that Trump groped a woman on a plane in the 1970s, the other that he behaved inappropriately in a beauty pageant dressing room.

But both simply cited news reports quoting eyewitnesses who vouched for Trump's behaviour.

Sanders has also repeatedly said the U.S. voters decided the merits of the allegations by electing Trump president.

Trump has also actively campaigned for Roy Moore, who was vying Tuesday for a seat in the Senate representing Alabama, despite historic allegations of predatory behaviour toward teen girls, including one accuser's allegation of an attempted sexual assault.

The Trump accusations surfaced during last year's presidential campaign, but the three women raised the issue anew on Megyn Kelly Today and at a news conference.

"It was heartbreaking last year," Holvey said. "We're private citizens, and for us to put ourselves out there to try and show America who this man is and how he views women, and for them to say, 'Eh, we don't care,' it hurt."

The former beauty queen claimed that Trump ogled her and other Miss USA pageant contestants in their dressing room in 2006. Crooks is a former receptionist at Trump Tower and Leeds says she met Trump on a flight.

Sixteen women have come forward with a range of accusations against Trump, many after the release of the Access Hollywood tape last October in which Trump was caught on an open microphone bragging about groping women.

One woman, Summer Zevos, a contestant on Trump's reality show, The Apprentice, sued, contending that Trump's denials of her accusations amount to false and defamatory statements.

With files from CBC News