Taoiseach Leo Varadkar has said that Karen Bradley's comments were insensitive and wrong.
It comes after the Northern Ireland Secretary apologised for the "offence and hurt" caused after she suggested deaths caused by British soldiers and police during the Troubles were not crimes.
"Legacy issues in Britain and Ireland are very difficult," Mr Varadkar said.
"I've met families who have lost loved ones during the Troubles and they're still grieving and seeking justice.
"In that context, I think the Secretary of State's comments were insensitive and they were wrong."
"Bear in mind we're talking about the killing of civilians, peaceful protesters in Derry on Bloody Sunday, we're talking about Ballymurphy and Kingsmills, and Dublin and Monaghan."
"We need a British Government that is at least open to the possibility that these killings of civilians were crimes.
"Indeed, there have been convictions for such killings."
Asked if Ms Bradley should resign, Mr Varadkar said: "Not gonna go there.
"It's not for me to determine the composition of any other government, that's something for the Prime Minister and Karen herself to decide."
Earlier: Karen Bradley 'profoundly sorry' for 'deeply insensitive' comments
Northern Ireland Secretary Karen Bradley has said she is "profoundly sorry" for "deeply insensitive" comments she made yesterday suggesting that deaths caused by soldiers and police during the Troubles were not crimes.
Ms Bradley faced calls to resign following the comments yesterday, which sparked criticism from victims of the security forces and nationalist political leaders, while the Government sought an explanation.
I am profoundly sorry for the offence and hurt that my words have caused
In her apology, Ms Bradley said her language was “wrong” and “deeply insensitive” to many of those who lost loved ones.
She said: “Yesterday I made comments regarding the actions of soldiers during the Troubles. I want to apologise. I am profoundly sorry for the offence and hurt that my words have caused.
“The language was wrong and even though this was not my intention, it was deeply insensitive to many of those who lost loved ones.
“I know from those families that I have met personally just how raw their pain is and I completely understand why they want to see justice properly delivered. I share that aim and that is why I launched the public consultation on addressing the legacy of the Troubles.
“My position and the position of this Government is clear. We believe fundamentally in the rule of law.
“Where there is any evidence of wrongdoing this should be pursued without fear or favour, whoever the perpetrators might be. That is a principle that underpins our approach to dealing with legacy issues and it is one from which we will not depart.”
Next week, prosecutors will announce whether soldiers will face trial for the Bloody Sunday killings of 14 innocent civilians in Derry.
Ms Bradley initially told British MPs on Wednesday: “The fewer than 10% (of killings) 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 Commons to say: “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.”
Tanaiste Simon Coveney says he met with Ms Bradley last night and told her the view of the government is that there should be effective investigations into all deaths during the Troubles regardless of the perpetrator.
Update: Karen Bradley's killings comments 'misguided and ill-judged'
The comments of Northern Secretary Karen Bradley in the House of Commons yesterday have been described as “misguided and ill-judged” by the sister of an IRA victim of the Troubles.
Ann Travers told RTE radio’s Today with Sean O’Rourke show that Ms Bradley’s comments had done nothing to help the healing.
“I just feel she’s put us all a step back,” she added.
Her sister Mary Travers was killed as she walked home from church with her mother and father who was a magistrate. She was aged 23 and worked as a primary school teacher.
“I’m not stupid, I realise that as time has gone on evidence has been lost or not stored properly and it is unlikely that anyone will ever end up in court.”
She told of she and her brothers had run from their home on hearing the shots and saw her injured parents and fatally wounded sister. “The memories will remain forever.”
As was the case with so many other families, the trauma and hurt was “so palpable, so real.”
She said she was horrified when politicians say things like Ms Bradley had said in the House of Commons.
Her comments were so stupid. They have done nothing to support those good men and women who were sent to Northern Ireland to do their job properly, who did not act criminally. She has done nothing to help them or us.
The SDLP’s Colum Eastwood told the same programme that Ms Bradley’s comments were “a very silly intervention.”
“I don’t understand how she could stand up and say those words and think there would be no impact.”
He said it was time for Ms Bradley to resign. “It is beyond acceptable for her to remain in that position.”
Professor of social policy at the University of Ulster, Deirdre Heenan said that the Northern Secretary’s comments were “grossly inappropriate” and that it appeared that the British Prime Minister Mrs May valued loyalty over capability.
Mr Eastwood added that it appeared Ms Bradley’s comments were part of the British government’s “cackhanded” attempts to influence the decision due next week from the Northern Ireland Public Prosecution Service about whether British soldiers will be prosecuted for the Bloody Sunday killings.
“This has been a long-running issue. State actors are trying to influence the issue.”
Ms Travers said that any process of reconciliation has to be holistic and be an all-island effort. However, she said she would find it very difficult to believe anything told to her by the IRA in a Truth and Reconciliation process.
I just don’t know. We need to start talking to each other, we have to start listening to each other, trying to build up relationships. We need to work on reconciliation.
Prof Heenan said that some people want or need the truth to move on, while others want justice. “The difficulty is that as time moves on memories fade. It looks like the British government is trying to let the clock wind down.
“Here the legacy of the past seeps into the future. The reality is they can’t go on fudging the issue. People like Karen Bradley need to take ownership of their words.”
Earlier: Bradley's comments 'like a colonial governor, lording over people', says brother of Bloody Sunday victim
The brother of a Bloody Sunday victim has described Northern Secretary Karen Bradley’s comments about killings by the British army as “like a statement from a colonial governor of the past, lording over people.”
Yesterday in the House of Commons, Ms Bradley said killings by the British army and police during the Troubles were “not crimes”.
Liam Wray, brother of 22-year-old Jim Wray who was shot by a British paratrooper on Bloody Sunday, told RTE radio’s Morning Ireland that he wasn't surprised at what she said.
“I was more surprised that she was so blatant and open about it, and it certainly was not a slip of the tongue.
"It wasn't a word out of place, it was a clear statement, like some colonial governor of the past lording over people to say it was not a crime for British soldiers to kill people here in Northern Ireland.
“It is horrendous that anybody could have an attitude like that in public life in the 21st century.”
When asked about Ms Bradley’s later clarification when she used a point of order to say that she was expressing a general view rather than referring to any particular case, Mr Wray said: “it sounded like a worm getting off the hook, she had pushed it too far and she realised that from the response she got.
“She thought she could get away with it, to say it was a slip of the tongue.
"It was certainly not a misunderstood statement, it was a clear statement that British soldiers did not commit crimes when they murdered people.
“Karen get honest, you meant what you said, it was clear, it was unambiguous, you came back then with a statement saying you were misunderstood, you were heard clearly.
It's not up for me to tell Karen Bradley to resign, if she was a woman of substance and a woman of dignity she would know what she should do herself.
Mr Wray described his brother’s death as “very savage. It was a very sad day for the family obviously and it's affected us for a long time.”