Omagh relatives have been given the brush-off by the Government in a hunt for answers about possible intelligence failures before the Real IRA massacre.
A Home Office Minister has told the Omagh Support and Self Help Group that the work of MI5 is "not relevant" to them.
The letter, from Minister of State Tony McNulty, is the latest in a series of refusals to engage with the relatives about their intelligence concerns.
Michael Gallagher, chairman of the Omagh group, said he believes the Government is trying to fudge the issue and keep MI5 "at arm's length" .
The Omagh families have sought answers from MI5 and the Home Secretary ever since the PSNI revealed that the Security Service was warned about a possible dissident attack on Omagh four months before the bombing that killed 29 adults and children, and two unborn babies.
MI5 acted on the warning - passed on by FBI informer David Rupert - and may have prevented an attack. But they did not tell the RUC that Omagh was a target, raising concerns about whether police could have responded differently to the attack.
Mr Gallagher, whose son Aidan died in the 1998 bombing, said the families are concerned about MI5's accountability - especially since the Security Service took over responsibility for national security in Northern Ireland last week.
"We are the first to recognise that there are areas that cannot and should not be talked about," Mr Gallagher said.
"But there has to be some degree of accountability. All we are asking for is a meeting with MI5, so that we can make our own minds up about any deficiencies in the intelligence services with regard to Omagh.
"I have to stress we haven't made our mind up - that's why the director of MI5 should meet the families, to discuss these matters.
"We understand why they have to be secret, but because they are taking over a wider role in Northern Ireland we feel there should be some degree of accountability."
He rejected Mr McNulty's suggestion that MI5's work is "not relevant" to the Omagh families.
Mr Gallagher said: "We're not experts, but we've experienced terrorism. To me, it's saying we're not important, and that's demeaning of the people who've stood up to terrorism and been counted. "
Last year, then director of MI5, Dame Eliza Manningham-Buller, refused to meet the families, and their requests for a meeting with previous Home Secretary John Reid also failed. The Home Office is directly responsible for the Security Service.
When Jacqui Smith became the new Home Secretary this summer, the families tried again for a meeting.
Mr McNulty responded this week, two months later. He offered to meet the families, but says he "will not be able to add substantially" to his comments in the letter.
Mr Gallagher said the Omagh families will "meet and discuss the offer Mr McNulty has kindly made to us, but we tend to think it would be a fudge".
In his letter, Mr McNulty said he appreciates the work undertaken by the Omagh Support and Self Help Group.