"If you have a neighborhood where there's a high level of gang activity, the way to prevent it is you increase the law enforcement presence there and you target the gang members to get them off the streets," the Texas senator told CNN's Anderson Cooper. "I'm talking about any area where there is a higher incidence of radical Islamic terrorism."
Cruz also pointed to what he called the "successful program" in New York implemented by New York Mayor Michael Bloomberg, apparently pointing to the New York Police Department's controversial surveillance efforts targeting Muslims under his administration.
J. Peter Donald, communications for the New York Police Department, described Cruz's comments as an "incendiary, foolish statement."
"Hey, @tedcruz are our nearly 1k Muslim officers a "threat" too? It's hard to imagine a more incendiary, foolish statement," he tweeted
, the night before Cruz is expected to host a rally in New York City.
Earlier in the day Cruz said in a statement, "We need to empower law enforcement to patrol and secure Muslim neighborhoods before they become radicalized," adding that the U.S. can no longer afford to "political correctness."
"For years, the West has tried to deny this enemy exists out of a combination of political correctness and fear. We can no longer afford either. Our European allies are now seeing what comes of a toxic mix of migrants who have been infiltrated by terrorists and isolated, radical Muslim neighborhoods," Cruz said in the statement.
Donald Trump said later Tuesday on CNN that he agreed with Cruz's proposal to target Muslim neighborhoods, calling it "a good idea."
Cruz's comments are not the first time the Republican presidential candidate has called for policies that would single out Muslims. The Texas senator argued in November that the U.S. should shut its doors to Muslim refugees from Syria, only allowing Christian refugees to seek asylum in the U.S.
Cruz's call drew a swift rebuke from GOP presidential rival Ohio Gov. John Kasich, Democratic National Committee Chairwoman Debbie Wasserman Schultz and the Anti-Defamation League, a leading anti-bigotry organization.
"We are not at war with Islam, we are at war with radical Islam," Kasich said during a news conference. "Just because you happen to be a Muslim does not mean you want to destroy someone in the West.... The last thing we need is more polarization because for those who want to preserve Islam in the west, we alienate them."
Still, Kasich argued the U.S. has been "too lax and not aggressive enough" in its response to terrorism.
Wasserman Schultz was blunter.
"Ted Cruz is a disgrace," the Florida congresswoman said, adding that the freshman senator's statement amounted to "fear-mongering."
"His comments today were worse than opportunistic and inappropriate politicking in the wake of the terrible tragedy in Brussels -- they were a shameful display of hate that only serves to foment anger and make the world less secure," Wasserman Schultz said in a statement.
Cruz campaign spokeswoman Alice Stewart said that a stepped-up police presence in Muslim neighborhoods "will both identify problem spots and partner with non-radical Americans who want to protect their homes."
And she reiterated that the U.S. cannot allow "political correctness to drive decisions about our security" and warned that a failure to act would result in problems of radicalization that authorities are dealing with in some Muslim neighborhoods in Europe.
"Innocent, peaceful Americans, no matter their faith, deserve to live in safe neighborhoods; that is what law enforcement exists to do, and that includes preventing radical Islamic terror cells from taking root in them. The police should have every tool available to follow leads and take action against those who would do us harm," she said in an email.
The Anti-Defamation League condemned Cruz's proposal in a statement Tuesday that said "demonizing all Muslims is a misguided and counterproductive response to the terrorist threat.
"Ordering special patrols of Muslim neighborhoods will almost certainly create an adversarial relationship between law enforcement and the communities they have sworn to protect, making those communities more vulnerable, more frightened, and often less willing to help. The approach is contrary to the principles of individual rights, equality, justice, and religious freedom on which this nation was founded," ADL CEO Jonathan Greenblatt said in the statement.
While Kasich and Cruz have both called for stops on resettling Syrian refugees in the U.S., neither have gone as far as Republican front-runner Trump who has called for banning all foreign Muslims from entering the U.S.
Cruz has said he disagrees with Trump's proposal, but also said he "understands" why the real estate mogul called for the ban.