WASHINGTON — For more than three decades, the Republican Party brand has been deeply tied to a worldview in which the aggressive use of American power abroad is both a policy imperative and a political advantage.

Now, a new generation of Republicans like Senator Rand Paul of Kentucky is turning inward, questioning the approach that reached its fullest expression after the terrorist attacks of Sept. 11, 2001, and signaling a willingness to pare back the military budgets that made it all possible.

That holds the potential to threaten two wings of a Republican national security establishment that have been warring for decades: the internationalists who held sway under the elder President George Bush and the neoconservatives who led the country to long and costly wars in Iraq and Afghanistan under President George W. Bush.

Members of both camps said this week that they fear returning to a minimalist foreign policy, as articulated in different ways by Mr. Paul, Senator Mike Lee of Utah and Representative Justin Amash of Michigan. The foreign policy hawks fear it would lead to a diminished role for America in an increasingly unstable world. And they worry about their party losing its firm grasp of what has traditionally been a winning issue.