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The rise of the Islamic State in the Middle East has pushed Republicans toward embracing a more interventionist foreign policy, and now one prominent Republican family wants to be sure the party stays that way.

Former Vice President Dick Cheney and his daughter Liz Cheney are planning to make their presence felt in the 2016 presidential campaign through their advocacy group, Alliance for a Strong America.

The organization is planning online and perhaps television ads pushing a muscular line on national security, according to a Republican strategist familiar with the group’s planning. The initiative may also pay for polling to help nudge Republican candidates toward hawkish stances in the primary season.

What is not clear, though, is whether the Cheneys intend to train their fire on Hillary Rodham Clinton or whether they plan to target Senator Rand Paul, the libertarian-leaning Kentuckian who has recently sought to bolster his White House campaign by trying to block a renewal of parts of the Patriot Act.

Mr. Cheney criticized Mr. Paul as “an isolationist” in an interview published online Sunday in The Wall Street Journal, which first reported the Alliance for a Strong America’s plans.

Asked about the assessment, Mr. Paul’s top political adviser questioned Mr. Cheney’s conservative credentials.

“Anyone who defends warrantless spying on innocent U.S. citizens, like President Obama, has no right to call themselves a freedom-loving conservative,” said Doug Stafford, the adviser to Mr. Paul. “Worse is these people are defending and supporting a program that the courts have said is illegal and the F.B.I. reports hasn’t led to a single terrorist arrest or thwarted terror plot. It has only resulted in the trampling of Americans’ rights.”

The harsh back-and-forth between the Cheneys and Mr. Paul’s orbit illustrates not only the tension in the party over how to balance defense and civil liberties, but also, as Mr. Stafford notes, basic questions about what it means to be a conservative on matters of national security.

The resurgence of radical Islamic terrorism in the Middle East may have pushed many primary voters toward a more hawkish orientation, but Mr. Paul’s success in at least temporarily stopping the N.S.A.’s use of metadata suggests that Republicans are uneasy with some of the intelligence policies put into effect during Mr. Cheney’s time as vice president.

Republicans who have spoken with Mr. Cheney, who represented Wyoming in the House for 10 years and who maintains an intense interest in both policy and political intrigue, say he is plainly concerned about the party backing away from intelligence programs.

Selective about his public appearances, Mr. Cheney is engaged in the 2016 presidential race behind the scenes. When aides to many of the leading Republican candidates descended on Wyoming this year to make their pitch to a group of wealthy donors, some of the staff members were surprised to find Mr. Cheney in the audience.