The shadow home secretary refused to take the list from presenter Andrew Marr as she attempted to defend her decision not to support the outlawing of groups, including those that had killed “a lot of people”.
Ms Abbott also defended comments she made backing the IRA in the 1980s as she bizarrely said her “afro and some of her views” had disappeared since then.
Speaking on the Andrew Marr Show, the host said: “In your career in the House of Commons you voted again and again around 30 times against anti terrorist legislation for different reasons.
“Shortly before 9/11 you voted against prescribing Al Qaeda as an organisation, that was a huge mistake on your part, was it not?”
Andrew Marr criticised Diane Abbott for not voting to ban
Well there is the list, which of those organisations do you think should not have been prescribed?
Ms Abbott replied Tory MPs including Theresa May also voted against certain terror measures including the 2005 Prevention of Terrorism Bill, ID cards and control orders without sufficient legal intervention.
“Nobody votes against these things without a lot of thought and the view of myself and Jeremy and most members of the Conservative Party including David Davis at the time was that this was counter productive, counter terrorism legislation,” she said.
Marr then reeled off a list of “dangerous” groups around the world that Abbott refused to prescribe.
In response, an uncomfortable Abbott said: “There were groups on that list which I deemed to be dissidents rather than terror organisations.
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Labour Leader Jeremy Corbyn takes part in a community meeting at the Guru Har Rai Gurdwara Sahib temple
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Britain's opposition Labour Party leader Jeremy Corbyn speaks at an anti-racism rally in London
“You have to give people credit for thinking about how they vote.”
Offering her the list, Marr then pushed the shadow cabinet member on which groups she would want to see banned.
He said: “Well there is the list, which of those organisations do you think should not have been prescribed?
“You voted against the whole lot being prescribed because presumably some of them you thought were ok. I’m just wondering which ones you think are ok.”
Refusing to take the list, Ms Abbott replied: “It’s not that I thought they were ok, I thought that they were dissident organisations.”
Asked if she regretted her support for the IRA back in the 1980s, she added: “It was 34 years ago, I had a rather splendid afro at the time, I don’t have the same hairstyle and I don’t have the same views.
“It is 34 years on, the hairstyle has gone and some of the views have gone.”
Ms Abbott was also lambasted by a Channel 4 News host who challenged her whether she identifies as British.
The shadow home secretary refused to answer outright whether she felt British but said she was “proud to be a British member of parliament”.