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.
More top news
President Trump went ahead on Monday with a tax hike on $200 billion (£152 billion) of Chinese imports.
The retailer said the biggest risk to the business was the likelihood of queues and delays at UK and EU ports.
In Northern Ireland and western Scotland it will cloud over, with outbreaks of rain and strong winds into the afternoon.