As the Texas governor stood by his remarks, the U.S. State Department distanced the Obama administration from the comments. Turkey's Ministry of Foreign Affairs decried the comments as "unfounded and inappropriate."
"Those individuals who are candidates for positions requiring responsibility such as the U.S. presidency are expected to be more knowledgeable on global affairs and more careful in their statements," the ministry said in a statement. "Turkey became a member of NATO when the governor was just 2 years old. ... The U.S. has no time to lose with such candidates who do not even know America's allies."
U.S. State Department spokesman Mark Toner described Turkey as a "stalwart ally" and said "we absolutely and fundamentally disagree" with Perry's comment on the country being run by Islamic terrorists.
At the debate, Perry was asked whether Turkey still belongs in NATO.
"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 to be in NATO, but it's time for the United States, when we look at their foreign aid, to go to zero with it," he said.
The exchange at Monday night's Fox News debate in South Carolina, while drawing condemnation from several corners, nevertheless brought to the fore some disturbing trends inside Turkey. Though there are indications Turkey has started to return to the Western orbit after flirting with Iran, the Islamist-leaning government has presided over a troubling record.
In the realm of press freedom, the country now ranks close to Russia, according to Reporters Without Borders. Dozens of journalists have been arrested this year, and thousands of websites have been blocked.
Turkey last fall expelled Israel's ambassador, following tensions over the deadly Gaza flotilla incident in 2010 in which Turkish nationals were killed in a confrontation with Israeli soldiers.
Meanwhile, Turkish officials recently met with a Hamas leader as part of talks reportedly aimed at reconciliation between Hamas and Fatah in the Palestinian territories.
Violence against women in the country has received considerable attention. According to one official report, the murder rate of women rose 1,400 percent from 2002 to 2009. And the country's internal affairs are dizzying, as a top former Army official was arrested earlier this month amid allegations of trying to topple the government -- allegations the official, Ilker Basbug, reportedly denies.
Soner Cagaptay, director of the Turkish Research Program with the Washington Institute for Near East Policy, wrote in a recent essay that the Turkish government has "neutered domestic checks and balances" since 2002, a "consolidation of power" that could have consequences for its relationship with the U.S. He noted that Turkish officials have demonized Western nations, and polls show the Turkish people mostly do not view the U.S. favorably.
Even so, Cagaptay said in an interview with FoxNews.com, Perry's comments were "far-fetched."
"Are there problems with Turkey's democracy? Yes," he said. But he described Perry's debate comments as inaccurate or overstated on several fronts.
First, Turkey does not receive U.S. foreign aid. "Some time in the 1980s it was phased out, so this is not your mother's Turkey," he said.
And he said the Islamic terrorist claim was "highly exaggerated."
As for the questions about Turkey's NATO membership, Cagaptay noted that Turkey has been aligned with the West regarding the protests in Syria and has agreed to host part of the NATO missile shield.
"I think that's a very serious commitment shown to the organization," he said, adding that the Arab Spring and the security threats it poses to the region might serve to bring Turkey closer to the West and NATO.
Perry stood by his comments on Tuesday.
"When you see the number of actions against your citizens that we would consider to be terrorist acts, I stand by my statement," Perry said. "You need to be putting protections in place for your citizens if you're seeing those types of attacks against, particularly, well, particularly females. That is particularly heinous from my perspective."
Campaign spokesman Ray Sullivan echoed the candidate's remarks.
"The debate question was specifically about the increased Islamist influence in Turkey, violence against civilian women in Turkey and association with Hamas," Sullivan said in a written statement. "Turkey can be a valuable ally, but the actions of the current government undermine that country's role in an organization like NATO. We need to send the message to Turkey that internal violence, association with terrorist groups and radical Islamist influence are inconsistent with being a NATO ally and positive player in world affairs."
Of the five remaining candidates in the GOP presidential race, Perry is polling last in most South Carolina polls.