Next week, prosecutors will announce whether soldiers will face trial for the Bloody Sunday killings of 14 innocent civilians in Londonderry.
When asked on Wednesday evening if she would like to apologise for her comments, Ms Bradley told the Press Association: "Coming back to the House of Commons and correcting the record is the biggest statement I can make in terms of the inadvertent comments that I made during oral questions.
"I was absolutely determined to be clear to everybody that what I had said needed correcting and to do so on the floor of the House of Commons is the biggest statement I can make."
She said she did not intend to cause "any offence or upset to anybody", adding: "I am determined that we will find a way to deal with the issue of the legacy of the Troubles in Northern Ireland as soon as possible and in a way that is right and fair for victims and everyone."
Pressed on whether she would say sorry to people she upset, Ms Bradley, who was at a Saint Patrick's Day event at the Embassy of Ireland in London, said: "As I say, I never intend to cause any offence.
"I want to ensure that we have a system that works for everyone."
Ms Bradley initially told MPs on Wednesday: "The fewer than 10% that were at the hands of the military and police were not crimes.
"They were people acting under orders and under instruction and fulfilling their duties in a dignified and appropriate way."
She later returned to the House of Commons to make clear her position, saying: "The point I was seeking to convey was that the overwhelming majority of those who served carried out their duties with courage, professionalism and integrity and within the law.
"I was not referring to any specific cases but expressing a general view.
"Of course where there is evidence of wrongdoing, it should always be investigated - whoever is responsible.
"These are of course matters for the police and prosecuting authorities, who are independent of Government."
Irish Foreign Affairs Minister Simon Coveney, who was also at the event at the Embassy of Ireland, was due to meet Ms Bradley to seek clarification.
A spokesman said: "Secretary of State Bradley's reaffirmation this afternoon that 'where there is evidence of wrongdoing, it should always be investigated - whoever is responsible' is important.
"There are no amnesties from prosecution provided for in the Good Friday Agreement or any subsequent agreements including the Stormont House Agreement.
"The Irish Government has been clear that it would not support any proposal to introduce such a measure, for state or non-state actors."
Mickey McKinney, whose brother William was shot by a Parachute Regiment soldier, said of Ms Bradley's initial comments: "It's very hurtful.
"She should resign right away, is she not aware that there was an inquiry that found our people completely innocent, was she not aware of David Cameron's apology to the people for the behaviour of the army?
"For her to come out with ridiculous comments, that is completely outrageous."
More than 90% of deaths caused during 30 years of violence involved republican or loyalist paramilitaries.