Any new memorial to victims of the 1998 Omagh bomb must represent what really happened, relatives have said.
An artist's impression of the Memorial Garden and the mirrors
Spokesman Michael Gallagher said they were happy with the statue, but were still in dispute with Omagh District Council over wording for a plaque.
The council said it had appointed an independent mediator in an attempt to reach an agreement with the families.
A design for the memorial was unveiled by the council on Tuesday but none of the families attended the event.
The victims' families claim that the Sinn Fein-dominated council object to having the words "dissident republican car bomb" on a memorial plaque.
The council said nothing had been ruled in or ruled out.
Mr Gallagher lost his son Aidan when a Real IRA bomb exploded in the County Tyrone town on 15 August 1998. Twenty-nine people, including a woman pregnant with twins, died.
He said: "We will take appropriate action to make sure the truth is told.
"Some people might view that as a threat, but if the truth is a threat people can judge for themselves.
"We will have no choice other than to address the issue ourselves.
"There can be no ambiguity over what happened on August 15 1998, and no dancing around words can distract from the truth."
Omagh District Council chief executive Danny McSorley said he wanted the views of everyone to be taken into account.
He confirmed the council would appoint an independent professional facilitator to lead a series of discussions involving all those affected by the atrocity on the issue of a narrative and to prepare a report for consideration.
The decision was taken in recognition of the wide range of views on the subject and in an attempt to reach a successful and consensual outcome, he added.
A competition was launched in April to provide a permanent tribute at the bomb site and nearby memorial garden.
The winning design was submitted by a Dublin team, artist Sean Hillen and architect Desmond Fitzgerald and its theme is "Constant Light".
It includes a 4.5m tall glass obelisk with a heart inside which will mark the site of the explosion.
Because of its position, the pillar is almost constantly in the shade.
But the designers plan to get around this with the use of 31 mirrors placed in the Memorial Garden around the corner - each one mounted on top of a pole, representing those who died.
Light reflected from these will be beamed down the street and onto the heart inside the pillar.
The memorial is expected to be ready in time for the 10th anniversary of the bombing.