Downing Street has said the "tragic" case involving British Army veteran Dennis Hutchings has illustrated the problems of pursuing historic allegations through the courts.
Mr Hutchings died in Belfast on Monday at the age of 80 after contracting COVID-19 while on trial over a shooting during the Troubles.
He had pleaded not guilty to the attempted murder of John Pat Cunningham and also denied a count of attempted grievous bodily harm with intent.
Mr Hutchings' trial had already been adjourned for three weeks after he caught coronavirus.
In a statement, the Cunningham family said they wished to acknowledge that this is a difficult time for the Hutchings family, adding they should be given time to grieve and will respond in greater detail in due course.
The Prime Minister's official spokesman said: "Our sincere condolences go to the family, friends and loved ones of Dennis Hutchings.
"The Ministry of Defence supported Mr Hutchings throughout his trial with legal representation and pastoral care, and that will continue to be offered to his family.
"This tragic case highlights that the criminal justice approach broadly is no longer working and that is why we are committed to introducing new legislation to bring greater certainty for all communities, including the veterans and families of victims."
In July, the Government announced plans for a statute of limitations that would end all prosecutions for Troubles incidents up to April 1998.
Military veterans, as well as ex-paramilitaries, would be protected from prosecution under the proposals, which would also end all legacy inquests and civil actions related to the conflict.
The Prime Minister's spokesman said: "We are engaging with the Irish government, with Northern Ireland parties and others to discuss how to address the legacy of the past in Northern Ireland, and our objective is to find an agreed way forward that will allow this legislation to be introduced."
On Tuesday, Northern Ireland's Public Prosecution Service defended its decision to prosecute Hutchings, saying the decision to prosecute was taken after an "impartial and independent application of the Test for Prosecution".
Dennis Hutchings had been suffering from kidney disease and the court had been sitting only three days a week to enable him to undergo dialysis treatment between hearings in Belfast.
Former Veterans Minister Johnny Mercer, who had accompanied Mr Hutchings to Belfast, said he was "fiercely proud" of the 80-year-old former soldier and "devastated" by his death.
"He was determined to prove his innocence against the unrelenting efforts of those who wish to rewrite the history of the conflict in Northern Ireland," Mr Mercer tweeted.
Ulster Unionist Party leader Doug Beattie has called for a "full and thorough" review into the decision-making of the Public Prosecution Service.
Raymond McCord, whose son was killed by loyalist paramilitaries in north Belfast in 1997, said he cannot understand politicians criticising the justice system, adding that what Dennis Hutchings faced was done in a "democratic fashion" through the courts.