The Republican, who is considering a presidential campaign in 2016, later defended — and repeated — the statement after facing reporters' questions about his claims.
In a speech prepared for delivery at a British think tank, Jindal said some immigrants are seeking "to colonize Western countries, because setting up your own enclave and demanding recognition of a no-go zone are exactly that." He also said Muslim leaders must condemn the people who commit terrorism in the name of faith as "murderers who are going to hell."
Jindal aides said he did not make significant changes to the prepared text.
The claims on "no-go zones" are similar to those a Fox News guest made last week about places where non-Muslims were not welcome in parts of the United Kingdom such as Birmingham, and "Muslim religious police" enforce faith-based laws.
Steven Emerson, an American author who often is asked about terror networks, told Fox News that in Britain "there are actual cities like Birmingham that are totally Muslim, where non-Muslims just simply don't go in."
Prime Minister David Cameron responded by calling Emerson a "complete idiot."
Emerson later apologized and said his comments "were totally in error." Fox News also issued apologies for broadcasting the comments.
Jindal, however, used similar rhetoric during a speech, warning of "no-go zones" in London and other Western cities. Jindal's remarks come in the wake of the massacre by Islamic extremists at a Paris magazine's offices and subsequent attack on a kosher supermarket in the city. Three gunmen killed 17 people in the attacks.
"I knew that by speaking the truth we were going to make people upset," Jindal told CNN during an interview from London.
"The huge issue, the big issue in non-assimilation is the fact that you have people that want to come to our country but not adopt our values, not adopt our language and in some cases want to set apart their own enclaves and hold onto their own values," said Jindal. "I think that's dangerous."
Jindal's parents immigrated to the United States from India. As a young man, Jindal converted from Hinduism to Catholicism.
Asked for evidence of "no-go zones," Jindal pointed to a weekend article in The Daily Mail, a London tabloid, that said killings, sexual abuse of minors and female genital mutilation are believed to go unreported to local police in some areas. The article did not give specific religious groups or towns.
"The bigger point is that radical Islam is a threat to our way of life," Jindal said. Asked if he regretted talking about "no-go zones," Jindal replied: "Not at all."
Jindal spoke to the Henry Jackson Society, a British think tank named for a former U.S. Democratic senator from Washington state who was a presidential candidate in the 1970s