Families' reaction: Mrs Geraldine Finucane said the British government decision was expected but still disappointing. She accused the government of ongoing delaying tactics and vowed that the campaign for an inquiry would continue.
"Justice Cory's report confirms that there was a state policy of targeting and assassination. The public should read details in his report.
"It is unbelievable, but the official documents that he examined show that it is all true."
Asked if she was angry, she replied: "Of course I'm angry. I'm tired of the delay."
Mr Barra McGrory, solicitor to the family of Ms Rosemary Nelson, said: "We are deeply affected by the apparent abject failure of the Northern Ireland office, and of the chief constable at the time, to take seriously the death threats issued to Rosemary shortly before her murder.
"Had Rosemary been treated with the respect and dignity her professional position deserved, she might well be alive today."
Ms Diane Hamill, sister of Robert Hamill, said her family was pleased the British government would act on Judge Cory's recommendation. "For the last seven years this is all we have tried to get from the night that my brother was attacked and allowed to be murdered," she said.
"That is all we have ever asked. Judge Cory, a man of great integrity, has obviously agreed with us after his exhaustive research and now the British government has acknowledged the need to establish one."
A spokesman for Mr David Wright, father of the murdered Loyalist Volunteer Force leader Billy Wright, who was shot dead by the INLA in the Maze prison, told The Irish Times of his satisfaction that an inquiry had been ordered.
He said: "Judge Cory has raised a number of serious questions about the conduct and actions of the prison authorities and intelligence agencies."
Relatives for Justice, a group representing the bereaved following murders involving alleged collusion, said: "We believe that there exists deep fear about the far-reaching implications of any inquiry into Pat's (Finucane) killing that would undoubtedly expose many other killings of a similar nature and go to the heart of the British government, exposing collusion as a policy of the Thatcher administration."
The group said it believed this was the main reason for not announcing a Finucane inquiry.