The British government is to pay compensation to the families of those killed and wounded on Bloody Sunday.
British paratroopers opened fire on a civil rights protest in January 1972, killing 14 innocent people.
After the publication of the Saville Report last year, the British Prime Minister described what happened in the Bogside in 1972 as both unjustified and unjustifiable.
Lawyers representing families of many of those involved in the Bloody Sunday campaign wrote to David Cameron about the issue of compensation.
Britain's Ministry of Defence has replied to the lawyers, saying it wants to resolve the compensation question as quickly as possible.
It said: "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.
"We are in contact with the families' solicitors and where there is a legal liability to pay compensation we will do so."
Lord Saville released the landmark report last year, which criticised the British Army over the killings.
His panel ruled that the British Army fired first and without provocation. It found all 14 who died and the others who were injured been unarmed and were completely innocent.
The troops had also continued to shoot as the protesters fled or lay wounded on the ground. One father was shot as he went to tend to his injured son.
Soldiers had insisted they had only retaliated in an attempt to cover up the truth. The document was described as "shocking" by Mr Cameron.
"We found no instances where it appeared to us that soldiers either were or might have been justified in firing," the Saville report said.
"Despite the contrary evidence given by soldiers, we have concluded that none of them fired in response to attacks or threatened attacks by nail or petrol bombers. No one threw or threatened to throw a nail or petrol bomb at the soldiers on Bloody Sunday."
Victims have spent years campaigning for justice and the revision of an original inquiry into the massacre, which they branded a whitewash.