The families said the meeting had been heated at times
A meeting between Prime Minister Gordon Brown and the Omagh bomb families has been described as "heated".
They discussed claims in a BBC programme that intelligence agency, GCHQ, did not pass on information that could have helped in the investigation.
Michael Gallagher, who lost his son Aiden in the bombing, said the meeting had been "quite heated" at times.
"We made our views very clear. We felt the Government, the police service had failed the Omagh families," he said.
"In particular the Panorama programme raised questions that we felt Sir Peter and his review didn't answer."
But Mr Gallagher also said the prime minister "was very generous".
"He said that he didn't see any possibility of any criminal prosecutions - he would be prepared to change the law if he felt it would help - but felt that it wouldn't help," he said.
A Northern Ireland Office spokesperson said the prime minister had "listened carefully and said he would reflect on what he had heard".
In January, the Intelligence Services Commissioner, Sir Peter Gibson, said he found no evidence that information held by GCHQ could have prevented the August 1998 bomb.
Twenty-nine people were killed when a Real IRA car bomb exploded in the town.