Republican presidential candidate and Texas Sen. Ted Cruz stood by his proposal to patrol U.S. "Muslim neighborhoods" during CNN's Republican Town Hall in Wisconsin Tuesday night, repeating his assertion that this strategy worked in New York City.

Host Anderson Cooper pressed Cruz repeatedly on his stance, noting New York City Police Commissioner William Bratton had criticized Cruz's proposal.

"It is clear from his comments that Sen. Cruz knows absolutely nothing about counterterrorism in New York City," Bratton wrote in an op-ed in the New York Daily News. However, Cruz discounted Bratton, saying he is a member of the administration of "left-wing radical" New York City Mayor Bill de Blasio.

"There's a difference between Islam and Islamism," Cruz told Cooper. "Islamism is a political and theoretical philosophy that commands its adherents to wage violent jihad to murder or forcibly convert all infidels. And by infidels, they mean every one of the rest of us."

"Islamism is our enemy. And when President Obama and Hillary Clinton and the rest of the Democratic Party play this politically correct game of denying it, it means they don't fight effectively," Cruz proclaimed.

"You did talk about patrolling Muslim neighborhoods. You kept saying that worked in New York, but political correctness made the police stop that," Cooper said. "New York Police have pushed back on that. (New York City Police Commissioner William) Bratton said that was just complete bunk."

"The guy who ran that program that you said was such a big success says it didn't lead to any prosecution. There were no leads from it," he added.

Cruz said his statements were dismissed by de Blasio and his administration for political reasons.

However, Cooper said it was not only Democrats and de Blasio who said Cruz's claim was false. "The commander who oversaw the very program that you claim was a success in New York testified under oath that it didn't lead to any investigations."

Cruz insisted the program was a success.

"In New York, this was a successful program. It was set up under Mayor Michael Bloomberg to monitor and to work cooperatively with the Muslim community to prevent radicalization and to stop radical Islamic terrorist plots before it occurs," he said.

Cruz said there were a number of cases for which law enforcement teams made a difference in New York, such as a book store that was identified as a locus for radicalization.

"When Mayor Bill de Blasio got elected, he gave into political correctness and he shut it down," Cruz said. "If you want to stop radical Islamic terrorism, the answer isn't to go hang out in random neighborhoods, it is instead to focus on communities where radicalization is at risk."