The Ministry of Defence (MoD) announced compensation will be paid to those killed or injured on Bloody Sunday.
"We acknowledge the pain felt by these families for nearly 40 years, and that members of the armed forces acted wrongly. For that, the government is deeply sorry," said a MoD spokesman on Thursday. "We are in contact with the families' solicitors and where there is a legal liability to pay compensation we will do so."
However, some families of victims are reported to have rejected any compensation until there is at least one successful prosecution of a soldier.
The family of William Nash, who was 19 years old when he was killed, have rejected any offer of compensation, even if the perpetrators were brought to justice.
"It is repulsive, offensive. Not now or at any time will I accept money.
"I've already told my legal team I want to go forward with prosecutions." said Linda Nash, the sister of William.
Her sister Kate Nash said she believed her brother's life was "too worthwhile to accept monetary compensation".
"Nothing can compensate for his loss," she added.
"He was too precious. The only thing that can give me peace is if the perpetrators are brought to justice."
In 1972 British troops opened fire on a civil rights protest in Derry, killing 14 civilians and wounding many more. The day is still commemorated every year across Ireland as Bloody Sunday.
The Saville inquiry concluded in 2010, 12 years after being set up. It found that the killings had been unjustified and that the Army shot protesters without any provocation, which increased calls for justice for the victims.
Prime Minister David Cameron issued a formal state apology to the victims and their families.
“The government is ultimately responsible for the conduct of the armed forces, and for that, on behalf of the government and on behalf of the country, I am deeply sorry." said Cameron in 2010.
However he avoided questions on prosecutions when pressed on the issue at the time by the then Labour leader Harriet Harman.