Ms Rice said the senator had “put party and politics over her own stated principles” of supporting equal rights and legal abortions.
“I think in a way that I really regret saying, she has betrayed women across this country,” she said at the The New Yorker Festival in New York.
Ms Rice, who also served as US ambassador to the United Nations (UN) under the Obama administration, said she would decide whether to run for the Senate from Maine in 2020 after next month’s midterm elections.
It comes after Dr Christine Blasey Ford testified to the Senate Judiciary Committee that Mr Kavanaugh sexually assaulted her at a house party when the two were teenagers.
Shortly before the Supreme Court vote, Ms Collins said: ”I do not believe that these charges can fairly prevent Judge Kavanaugh from serving on the Court.”
However, she described Dr Ford’s testimony as “sincere, painful and compelling.”
The climactic 50-48 vote on Mr Kavanaugh on Saturday was the closest vote to confirm a justice since 1881. Every Democrat voted against Mr Kavanaugh apart from Joe Manchin of West Virginia.
Ms Collins has faced a backlash over her decision to support Mr Kavanaugh, with a crowdfunding page supporting any future opponent of hers raising more than $3.4m (£2.6m) of a £4m target by Monday morning.
Ms Rice hinted her interest in a Senate run in a Twitter post on Friday that was retweeted 38,000 times.
In a later post, Ms Rice said: “Many thanks for the encouragement. I’m not making any announcements. Like so many Americans, I am deeply disappointed in Senator Collins’ vote for Kavanaugh. Maine and America deserve better.”
Ms Collins responded to the former National Security Adviser’s comments in an interview with CNN.
Asked whether she could lose her seat over the Supreme Court vote, Ms Collins said: “I have to do what I think is right. Over the years the people of Maine have trusted me to exercise my best judgment. That’s what I did in this case.
“I’m going to do what I think is right. That’s what I owe my constituents. As far as Susan Rice is concerned, her family has a home in Maine but she doesn’t live in the state of Maine, everybody knows that.
“The irony is, back in 2009 when she was nominated to be ambassador of the UN, she came to me, even though I did not know her back then at all and pleaded with me to introduce her for the committee, which I was happy to do because her family had links to the state of Maine.”
When reminded about how Ms Collins had backed her to be ambassador to the UN on Twitter, Ms Rice said: “Thanks for recalling. I was very grateful for Senator Collins’ extremely generous endorsement of my nomination and her detailed description of my deep ties to Maine. 2009 seems like a long time ago now – on so many levels.”
Following the vote on Mr Kavanaugh, Senate majority leader Mitch McConnell insisted his chamber was not irreparably damaged by the bitter row. He signalled he was willing to take up another high court nomination in the 2020 presidential election season should another vacancy arise.
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