The TV presenter grilled the shadow home secretary as he said many would not want her to be own charge of the Home Office.
Speaking on The Andrew Marr Show on the BBC, Marr said after the Manchester bombing at an Ariana Grande concert last Monday night, voters did not believe her or Jeremy Corbyn should be in charge of the UK’s security.
He said: “A lot of people watching this programme, after Manchester, thinking of who to vote for look at you and look at Jeremy Corbyn and think ‘do you know what, we don’t completely trust you’ to be in charge of the security of this country, given what you have said in the past, some of the things you have done in the past.
“You can take a moment now to, as it were, talk to them and tell them why they’re wrong about you.
Andrew Marr said Britons did not "trust" Diane Abbott over the UK's security
People look at you and they say ‘I don’t trust Diane Abbott to be in charge of the Home Office'
“People look at you and they say ‘I don’t trust Diane Abbott to be in charge of the Home Office'.”
Ms Abbott defended her experience and said she knew how to look after the British public.
“First of all I think there’s something to be said for a Home Secretary who has actually worked in the Home Office,” she said.
“I worked in the Home Office for nearly three years as a graduate trainee and I know how it works from the inside.
Jeremy Corbyn in pictures Tue, July 12, 2016
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
“I think there’s something to be said for a Home Secretary who is a very young woman, worked and campaigned with diverse communities and sees these issues, not just from the point of view of bureaucrats but from the point of view of diverse communities.
“There’s also something to be said for a Home Secretary who’s spent 30 years as a constituency MP and knows how these issues impact on ordinary people.”
But Marr was not finished and referred to previous comments she made about scrapping MI5.
He said: “What about a Home Secretary who in the past has said we should abolish MI5?”
On the back foot, Ms Abbott said she had since changed her view.
“At that time, I and a lot of people felt MI5 needed reforming. It has since been reformed and of course I would not call for its abolition now,” she said.
The shadow home secretary refused to answer outright whether she felt British but said she was “proud to be a British member of parliament”.