Northern Ireland Secretary Karen Bradley has said she is determined to deliver for families hurt by comments she made about the Troubles.
She said on Wednesday that deaths caused by the security forces in Northern Ireland were "not crimes".
Speaking to the BBC's The View programme on Thursday, Mrs Bradley said she had "said the wrong thing".
When asked about whether she would resign, she said she was determined to deliver for people in Northern Ireland.
"What I do want to do now is make sure I deliver for those families, from all parts of the community, who have been so deeply affected by the Troubles," said Mrs Bradley.
"I know how raw that pain is and I'm devastated to think that I have made it worse."
'Corrected the record'
There were no excuses for what she said in the House of Commons on Wednesday, she said, adding: "It's not what I think, it's not what I mean."
"I said something in response to an oral question and as soon as I realised what I had said I corrected the record.
"I am determined that those families who have been hurt by what I said will see justice."
Mrs Bradley has faced considerable criticism for the remarks she made on Wednesday.
The Police Service of Northern Ireland's (PSNI) chief constable said on Thursday that a soldier or police officer should be investigated if they shot someone.
"Where people have lost their lives we should all be equal under the law," added George Hamilton.
"There should be a thorough and effective investigation."
'No regard for Troubles inquest'
Speaking at a high-profile Troubles-related inquest in Belfast, the leading barrister Michael Mansfield QC said Mrs Bradley had made "entirely inappropriate observations" on Wednesday.
The inquest is examining 10 people's deaths at Ballymurphy in August 1971, which followed three days of gunfire in west Belfast after the introduction of internment.
Mr Mansfield is representing some of the victims' families and previously participated in the Bloody Sunday and Hillsborough inquiries and the Birmingham Six case.
He told the coroner that Mrs Bradley clearly had "no regard whatsoever for these proceedings".
Analysis: Jayne McCormack, BBC News NI political reporter
After almost 24 hours of facing pressure to say sorry, Karen Bradley's statement may be too little, too late for some.
Although she has acknowledged that her language was wrong, she will still face questions as to why she ever made the remark in the first place.
Number 10 says it has full confidence in her as Northern Ireland secretary, who is a Theresa May loyalist.
It is also unlikely she will face pressure in London to step down.
The prime minister can hardly afford to lose another cabinet minister when she is in the throes of the last Brexit act.
But some politicians and victims' campaigners in Belfast and Dublin have said Mrs Bradley's apology does not cut it.
The Tánaiste (Irish deputy prime minister) Simon Coveney welcomed Mrs Bradley's apology and said he thought she recognised "the seriousness of the statement made yesterday".
"I made it perfectly clear to the secretary of state last night that I believed her statement was wrong, that it was ill-advised and that it would cause deep offence to many people."
Lord Dannatt, the former head of the Army, said Mrs Bradley should consider apologising over the comments but should not quit her role.
"It would not be unreasonable for her to offer an apology," he said.
"I think it's unnecessary for her to resign - there's enough confusion in our political world at the present moment."
Attorney General Geoffrey Cox defended the Northern Ireland secretary, telling the Commons that he "believed firmly" that she had not intended any offence.
The shadow Northern Ireland secretary Tony Lloyd called on Mrs Bradley to outline what the government "plans to do around legacy cases in Northern Ireland".
'Foot in mouth'
Ulster Unionist MLA and former Army officer Doug Beattie said that politicians must be mindful about what they say about Troubles legacy issues.
Politics had arrived at a "major tipping point", he added, and Mrs Bradley "should have been alive" to the fact that an announcement is due to be made on whether or not former soldiers should be prosecuted in relation to Bloody Sunday.
"She has clearly put her foot in her mouth... and I think she knows that," he added.
Mr Beattie said Mrs Bradley should apologise to the families of those who died on Bloody Sunday in Londonderry in January 1972.
Thirteen people were killed on Bloody Sunday after troops opened fire, and another died of his injuries some months later.
But Mr Beattie differentiated those events from the SAS killings of eight IRA men who were preparing to bomb a police station in Loughgall, County Armagh, in 1987.
"If you take the likes of Loughgall, that was force on force and was absolutely right," he added.
"Bloody Sunday was not and if there is evidence against those people who killed those innocent civilians then the law must be seen to run its course."
Victims' families have called for Mrs Bradley to resign.
John Kelly, whose teenage brother Michael was killed on Bloody Sunday, described her remarks as "outrageous".
John Teggart, whose father was killed in the 1971 Ballymurphy shootings, also said she should quit.