Ireland’s deputy prime minister has criticised Britain’s new defence secretary for making “loose comments” about introducing an amnesty against prosecution for British soldiers relating to incidents during the Troubles.

Simon Coveney was responding to Penny Mordaunt, who said on Wednesday that she thought her proposals to introduce a statutory presumption against prosecution for veterans for alleged offences committed than 10 years ago should encompass Northern Ireland.

Coveney told the Irish parliament that “we need to ensure loose comments that are made are not damaging in terms of trust” and said he expected the UK to uphold the commitments it had already made.

“There should be effective investigation into deaths during the Troubles, regardless of the perpetrators,” Coveney said. “That is what is provided for in the legacy framework of the Stormont House agreement and it is imperative that we move forward.”

He added that Karen Bradley, the UK’s Northern Ireland secretary, had written to him on 18 April saying that where there was evidence of wrongdoing relating to the Troubles, members of the British army should be prosecuted.

In the same debate, Michelle O’Neill, Sinn Féin’s deputy leader, said: “The comments made by Penny Mordaunt undermine the legacy mechanisms agreed by the two governments and five main parties at Stormont House [in 2014].”

Earlier this week Mordaunt announced plans to bring in legislation for a statutory presumption against prosecution of veterans relating to alleged crimes committed during the course of duty that took place more than a decade ago.

The proposals are likely to halt any future prosecutions of the military relating to the wars in Iraq and Afghanistan except in exceptional cases, but the Ministry of Defence initially said they would not apply to Northern Ireland.

The investigation of cases and possible prosecutions dating back to the Troubles, in which an estimated 3,500 people died over a quarter of a century, form part of a separate legacy review process being conducted by the Northern Ireland Office.

Earlier on Thursday, however, a string of Conservative MPs complained about the proposed Northern Ireland exemption in an emergency Commons debate.

Bob Stewart, a backbencher, told MPs that he had completed seven tours in Northern Ireland. “I was involved in fatality shootings. I was investigated along with others. The investigations were thorough, aggressive, and bloody awful to go through,” he said.

The debate had been prompted by an urgent question from Mark Francois, a former armed forces minister. He told MPs that he did not want to see Northern Ireland’s power-sharing executive re-established “at the price of some rancid backstairs deal between the Northern Ireland Office and Sinn Féin IRA [to allow the continued prosecution of soldiers over the Troubles]”.

John Penrose, a Northern Ireland minister, said any new proposals for veterans serving abroad could not simply be extended to Northern Ireland, because “the rules were different when soldiers were serving in Northern Ireland”.

He added: “They were there in support of the police and in support of civil powers, which forms a different legal basis than the one that applies if they are fighting abroad in other kinds of conflict.”

Any attempt to introduce a statute of limitations to one group in Northern Ireland, Penrose added, would have to apply to all, including alleged terrorists. Human rights law would mean it would “have to apply to all sides of the conflict”, he said.

Final proposals for dealing with the legacy of the Troubles in Northern Ireland, which include plans for a historical investigations unit, will be published later. Ministers are evaluating 17,000 responses to a consultation on the controversial topic.