(CNN) Louisiana Gov. Bobby Jindal on Monday stood by his criticism of so-called "no-go" zones in Europe, where sovereign nations allegedly cede authority to Muslim immigrants, a controversial idea that many critics say is overblown.

And the potential 2016 Republican presidential candidate decried what he called immigrants' insistence on "non-assimilation, the fact that "you've got people who want to come to our country but not adopt our values," which he called "dangerous."

Jindal has the reputation of policy wonk among Republicans and boldly told GOP officials during a 2013 address to the Republican National Committee that they "must stop being the stupid party" and needed to "stop insulting the intelligence of voters."

Asked by CNN's Wolf Blitzer whether he would walk back his comments on no-go zones, made in a speech to the Henry Jackson Society in London earlier that day, Jindal said, "not at all."

"And I'm also making a bigger and maybe even more controversial point that radical Islam is a grave threat, we need Muslim leaders to denounce the individuals, not just the acts of violence," he said, adding that "it is absolutely correct to insist on assimilation" of immigrants in the United States.

But pressed for specific examples of such no-go zones, Jindal demurred, saying he had met with "elected officials and others" to discuss them and noted a report in UK tabloid the Daily Mail that purported to highlight the challenges facing law enforcement in such areas.

"I knew by speaking the truth we were gonna make people upset," Jindal told Blitzer.

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Jindal was also unable to offer examples during an earlier interview with CNN's Max Foster, saying that he's "heard from folks here that there are neighborhoods where women don't feel comfortable going in without veils ... We all know that there are neighborhoods where police are less likely to go into."

"I think that the radical Left absolutely wants to pretend like this problem is not here. Pretending it's not here won't make it go away," he told Foster.

Pressed for details, Jindal said only, "I think your viewers know absolutely there are places where the police are less likely to go."

And asked whether that feeling may be caused by high crime rates, rather than the Muslim population in the area, Jindal said, "This isn't a question."

"I know the Left wants to make this into an attack on religion and that's not what this is. What we are saying, it's absolutely an issue for the UK, absolutely is an issue for America and other European and Western nations," he said.

During his London speech, Jindal said, "In the West, non-assimilationist Muslims establish enclaves and carry out as much of Sharia law as they can without regard for the laws of the democratic countries which provided them a new home," according to prepared remarks.

"It is startling to think that any country would allow, even unofficially, for a so-called 'no-go zone.' The idea that a free country would allow for specific areas of its country to operate in an autonomous way that is not free and is in direct opposition to its laws is hard to fathom," he said.

Jindal also suggested the rise of such no-go zones has contributed to growing anti-Semitism throughout Europe, which has prompted many Jews to emigrate from their home countries.

"How does such evil rise again in democratic countries?" Jindal asked. "I believe it is because radical Islamists have been given too wide a berth to establish their own nation within a nation," he said.

Muslim leaders need to "condemn anyone who commits these acts of violence, and clearly state that these people are evil and are enemies of Islam," he added.

The idea of "no-go zones" sparked controversy last week when a Fox News commentator raised the prospect of areas in France, Britain, Sweden and Germany where those countries' governments "don't exercise any sovereignty," and which instead are run largely by Muslim immigrants.

The commentator also mentioned whole cities "where non-Muslims simply don't go in," in particular the city of Birmingham in the United Kingdom.

British Prime Minister David Cameron later pushed back on the idea, calling the commentator "a complete idiot."

"When I heard this, frankly, I choked on my porridge and I thought it must be April Fools' Day. This guy is clearly a complete idiot," he said.

The Fox commentator later apologized to Birmingham for labeling it a no-go zone, but stood by the idea that such areas exist. Fox News, however, issued a formal apology for the remarks, with host Julie Banderas retracting the comments as "regrettable errors" and saying the network "deeply regret(s) the errors and apologize(s) to any and all who may have taken offense."

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But a Jindal aide said the governor stuck largely to the text as prepared, which included the criticism of the zones. And the remarks have drawn praise from conservatives and attacted national media attention at a time when the potential presidential contender is looking to raise his profile in time for a White House bid.

National Review columnist Larry Kudlow called it a "brilliant take on radical Islam."

"It is the toughest speech I have read on the whole issue of Islamic radicalism and its destructive, murdering, barbarous ways which are upsetting the entire world," Kudlow wrote in an op-ed.

Democrats, though, knocked Jindal.

"It's no surprise that Bobby Jindal would go abroad and butcher the facts in an effort to divide people -- this is exactly what we've come to expect from Jindal here at home," Democratic National Committee spokeswoman Rebecca Chalif told CNN. "Jindal is just embarrassing himself. He is abroad while Louisiana is facing a budget crisis of his own making -- he can't even govern his state, he is the last person we want wading into foreign policy."