The Northern Ireland secretary said in the House of Commons on Wednesday that killings carried out by the police and military during the Troubles were not crimes, rather actions of people “fulfilling their duties in a dignified and appropriate way”.
The claim prompted calls for her resignation from victims of state violence and several political parties in Northern Ireland.
In an interview with the Press Association in Belfast on Thursday evening, Bradley attempted to reach out to bereaved families, but her invitation to meet was swiftly rejected.
Bradley said there were “no excuses” for what she said, adding: “I recognise that a slip of the tongue at the wrong moment has caused enormous distress.
“I want to be very clear – I do not believe what I said, that is not my view.”
John Teggart, whose father Danny was shot 14 times at Ballymurphy, said Bradley should resign, adding: “Ballymurphy massacre families have been requesting a meeting with the secretary of state since she took up her position of Secretary of State for Northern Ireland.
“Karen Bradley hasn’t even replied to these requests. Tonight (Thursday) we find that she would like to meet us tomorrow to apologise for the hurt she has caused.
“We will not meet her, and have one request for Bradley and that is for her to resign immediately.”
The secretary of state’s remarks carried added significance as they were made a week before long-awaited decisions from Northern Ireland prosecutors on whether 17 soldiers involved in the Bloody Sunday shootings in Londonderry in 1972 will face prosecution.
Bradley made it clear on Thursday she would not be resigning over the gaffe, vowing to work to deliver for people she had offended.
“I want to get on and get this job done,” she said.
Downing Street has said prime minister Theresa May retains “full confidence” in her.