Perry, who is the governor of Texas, made the remarks at a debate in Myrtle Beach, South Carolina, ahead of primaries in that state for the Republican Party's presidential nomination.
"Well obviously, when you have a country that is being ruled by what many would perceive to be Islamic terrorists, when you start seeing that type of activity against their own citizens, then yes, not only is it time for us to have a conversation about whether or not they belong in NATO, but it is time for the United States, when we look at their foreign aid, to go to zero with it," Perry said.
Turkish Foreign Ministry spokesman Selcuk Unal said Ankara strongly condemns Perry's "unfounded and inappropriate allegations."
Turkey's Foreign Ministry earlier released a statement saying that Perry's comments were "baseless and inappropriate" and that the United States has no time to waste with candidates "who do not even know their allies."
The statement said that Turkey, who is a founding member of the trans-Atlantic alliance, "joined NATO while the governor was still 2-years-old."
U.S. State Department spokesman Mark Toner also rebuffed Perry's remarks today, saying the United States "absolutely and fundamentally" disagrees with Perry's comments.
Turkey is hosting NATO's early warning radar system as part of the alliance's missile-defense system, which is capable of countering ballistic missile threats from Iran.
Turkey has been ruled by a government with Islamist roots since 2002.
compiled from agency reports