Michael Gallagher, whose son Aiden, 21, was among the Omagh victims, condemned the decision, describing the reasons given by Ms Villiers for ruling out a public inquiry as "trivial".
He told Sky News: "Should we be denied truth and justice because other people don't want it?"
Referring to his belief that the bomb attack could have been prevented, he said: "The reality is that Aiden need not have died."
He added: "Both the British and Irish governments failed to protect the human rights of those people."
And he said that victims' families would be mounting a legal challenge to the decision by Ms Villiers.
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