The shadow home secretary refused to answer outright whether she felt British but said she was “proud to be a British member of parliament”.
Speaking on Channel 4 News, Ms Abbott was questioned by presenter Krishnan Guru-Murthy about her loyalty and “attitude towards Britain”.
He said: “Isn’t part of the problem perhaps not what you’re saying but who’s saying it? That there are ongoing worries about Mr Corbyn’s overall attitude towards Britain and your own.
“Let’s put the words that have been doing the rounds about you, decades ago admittedly.
“In 1984 you’ve been quoted as saying ‘every defeat of the British state is a victory for all of us’.
“Now you were talking about a Northern Ireland context, ‘a defeat in Northern Ireland will be a defeat indeed’. Why did you say that?”
Ms Abbott attempted to defend her comments by saying they were made over 30 years ago and she “now knew better”.
“Well that was 34 years ago and I said a number of things 34 years ago and I now know better as a member of parliament of 30 years standing,” she said.
Asked twice if she took the comments back, Abbott added: “I’ve moved on since 34 years ago, have you?”
But, not finished yet, Guru-Murthy then asked Ms Abbott, who was elected the UK’s first black woman MP, if she felt British.
He said: “You also said you couldn’t identify as British, can you now tell the voters that you do identify as British?”
Ms Abbott replied: “I was elected as a British member of parliament in 1987, I was the first black woman ever elected and I’m proud to say I’m a British member of parliament.
“I have no problem with that at all.”