Ms Abedin writes in her forthcoming memoir that the senator forcibly kissed her on a couch after inviting her up for coffee after a dinner in Washington DC between senators and their aides.
And she writes in wrote in her new book, Both/And: A Life in Many Worlds, that she was able to forget about the incident until 2018 when Christine Blasey Ford testified to Congress about her alleged assault by Supreme Court Justice Brett Kavanaugh.
Ms Abedin does not name the senator or his political party in the book, which is out next week.
She writes that the incident happened sometime after Donald Trump’s 2005 wedding to Melania Trump, after she had gone to the dinner with Ms Clinton.
“I ended up walking out with one of the senators, and soon we stopped in front of his building and he invited me in for coffee. Once inside, he told me to make myself comfortable on the couch,” she writes in the book, which was obtained by The Guardian.
She said the senator took off his blazer and made coffee before sitting down beside her on the couch.
“Then, in an instant, it all changed. He plopped down to my right, put his left arm around my shoulder, and kissed me, pushing his tongue into my mouth, pressing me back on the sofa.
“I was so utterly shocked, I pushed him away. All I wanted was for the last 10 seconds to be erased.”
Ms Abedin said that the senator apologised to her and admitted he had “misread” their relationship as she worked out a way to leave “without this ending badly.”
“Then I said something only the twentysomething version of me would have come up with – ‘I am so sorry’ – and walked out, trying to appear as nonchalant as possible,” she wrote.
She says in the book that she suppressed her memory of the incident until she read about Ms Ford “being accused of ‘conveniently’ remembering” her alleged assault after Mr Kavanaugh was nominated for the high court by Donald Trump.
Ms Ford alleged that Mr Kavanaugh assaulted her at a high school party, which he strongly denied before being confirmed to the bench.
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