WASHINGTON — Half a dozen Democratic senators have called on President Donald Trump to resign over sexual misconduct allegations. On Tuesday morning he singled out one of them for attack — New York Sen. Kirsten Gillibrand — and with a sexually suggestive tweet that immediately provoked new criticism.Trump wrote that “Lightweight” Gillibrand “would come to my office ‘begging’ for campaign contributions not so long ago (and would do anything for them).”

Although provocative tweets are commonplace for Trump, this one hit a political nerve given national attention to the topic of sexual harassment of women and renewed scrutiny of the allegations against him by more than a dozen women. Social media and cable television talk shows quickly ignited with bipartisan outrage.

Hours later, Trump’s top spokeswoman denied that he implied anything sexual. “Only if your mind is in the gutter would you have read it that way,” Sarah Huckabee Sanders told reporters.

Sanders said Trump was merely talking about how Gillibrand is beholden to those who donate to her election campaigns, calling her a “wholly owned subsidiary” of her donors.

“There’s no way that this is sexist at all,” Sanders said.

Gillibrand, who is mentioned as a possible presidential candidate for 2020, hit back at Trump. She said in a tweet that he has brought “shame” to the presidency and “cannot silence” her or the women who have described his alleged misconduct. Separately, she told reporters Trump’s words were “a sexist smear.”

At least 16 women came forward before his election to describe Trump forceably kissing or touching them, or purposely walking in on them in dressing rooms, among other allegations. Three of the women called on Monday for a congressional investigation into their claims, in a bid to take advantage of the current climate against sexual misconduct.

Trump described the accounts as “false accusations and fabricated stories” in another tweet on Tuesday, saying they came from “women who I don’t know and/or have never met” — a contention some of the women dispute.

Of six Democrats who have said Trump should quit, two are women. Trump’s jabs solely at Gillibrand, which came after she tweeted Monday night that he should resign, fit into the president’s longtime pattern of lashing out and belittling his critics.

Katie Packer Beeson, a veteran Republican strategist and Trump opponent, said Trump’s tweet was indicative of how he “views women and the way he bullies and demeans those who he views as a threat.”

Sanders noted that Trump targets men and women alike. Indeed, last year Trump used similar innuendo to denigrate Mitt Romney after the 2012 Republican presidential nominee said then-candidate Trump didn’t have the temperament to be president. Trump countered that Romney was “begging” for his endorsement in 2012, adding, “I could have said, ‘Mitt, drop to your knees.’ He would have dropped to his knees.”

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Mary Anne Marsh, a Democratic strategist, said Trump seems “to come undone” whenever someone questions his ability to be president.

“If it is a woman calling into question if he should be in office, he really comes undone,” Marsh said, pointing to Trump’s attacks on Hillary Clinton, journalist Megyn Kelly and MSNBC host Mika Brzezinski.

Marsh said Trump’s outburst may have had the unintended effects of mobilizing women voters and elevating the national profile of a potential 2020 rival, Gillibrand.

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Democratic lawmakers rallied to Gillibrand’s defense.

“It took my breath away and it represents the conduct of a person who is ill-equipped to be the president of the United States,” said Rep. Jackie Speier of California, who helped get more than 100 House Democrats to sign a letter demanding a House investigation of the allegations against Trump.

“He was disgusting. It was clear what he was getting at,” Massachusetts Sen. Elizabeth Warren told reporters. Sen. Richard Blumenthal of Connecticut said Trump’s tweet was a “sexist slur that disgraced the office and diminishes the presidency.”

Republicans mostly sought to avoid the latest contretemps. Asked whether Congress would investigate allegations against Trump, Senate Majority Leader Mitch McConnell said, “What we’re in charge of here is the Senate.”

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(Sarah D. Wire of the Tribune Washington Bureau contributed to this report.)