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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.
Explaining the decision to reject calls for a public inquiry into the 1998 Omagh bombing, Northern Ireland Secretary Theresa Villiers said in a statement:
The Government will not launch a public inquiry into the events surrounding the Omagh bombing in 1998, it was announced today.
"After consultation and careful consideration, I have decided not to instigate a public inquiry into the circumstances surrounding the bombing in Omagh on 15 August 1998," Secretary of State for Northern Ireland Theresa Villiers said.
"The current investigation by the Office of the Police Ombudsman for Northern Ireland is the best way to address any outstanding issues relating to the police investigation of the Omagh attack."
The car bomb was an attempt to disrupt the peace process, killing 29 and injuring more than 200.
No criminal convictions have been made in connection with the attack.
Latest ITV News reports
The Government has ruled out a public inquiry into the Omagh bomb attack in August 1998 that killed 29 people.