New York -- Hours after terrorist explosions in Brussels killed at least 31 people, Republican presidential candidate Ted Cruz proposed that law enforcement increase monitoring of Muslim neighborhoods in the U.S.

In a statement released by his campaign, Cruz wrote: "We need to empower law enforcement to patrol and secure Muslim neighborhoods before they become radicalized."

Cruz said European nations have seen the consequences "of a toxic mix of migrants who have been infiltrated by terrorists and isolated, radical Muslim neighborhoods."

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"We know what is happening with these isolated Muslim neighborhoods in Europe. If we want to prevent it from happening here, it is going to require an empowered, visible law enforcement presence that will both identify problem spots and partner with non-radical Americans who want to protect their homes," the Cruz campaign clarified in a statement.

John Kasich, a Republican rival to Cruz's presidential ambitions, pushed back on the proposal, saying the effort would add "more polarization" and "create divisions" in the U.S.

"I don't know whether this is true or not, but Cruz said we should start patrolling Muslim neighborhoods or something - is that true?" Kasich asked a group of reporters outside of a campaign stop in Minneapolis.

He added: "In our country, we don't want to create divisions where we say, 'Okay, well your religion -- you're a Muslim, so therefore we're going to keep an eye on you."

Bernie Sanders on Tuesday afternoon called the the notion "unconstitutional" and "wrong."

And the Council on American-Islamic Relations (CAIR) compared it to "the dark days of the 1930s" in Europe, calling it "a very frightening image."

"What is a Muslim neighborhood? How many Muslims have to be in a neighborhood before it becomes worthy of checking papers and kicking in the doors of homes and businesses?" Ibrahim Hooper, spokesman for CAIR, told NBC News. "What constitutes a Muslim neighborhood?"

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Hooper - exasperated in the phone call -- called "anti-Muslim bigotry" a "Republican thing."

"Each day you wonder what the next bizarre and unconstitutional policy proposal will come out of the Republican side of the presidential campaign," Hooper said. "It's really astounding."

Last week, Cruz named nearly two-dozen foreign policy advisers he confers with on issues of national security. Several have drawn harsh criticism for their views of Muslims.

One of those is Frank Gaffney, a former Reagan administration official and now an adviser to Cruz, who asserts that the Muslim Brotherhood penetrates and manipulates the U.S. government and the Republican Party. And Gaffney hasadvocated for a congressional panel to investigate treason by American-Muslims, like the House Un-American Activities Committee that operated during the first several decades of the Cold War to identify threads of communism in the U.S.

Another adviser, Clare Lopez, who works at the same organization founded by Gaffney, recently suggested Sen. Joseph McCarthy was "absolutely spot on in just about everything he said about the level of infiltration" of communism and said affiliates of the Muslim Brotherhood are the "go-to advisers, if not appointees" in the Obama administration.

In an interview on CNN on Monday, Cruz suggested criticisms over his controversial advisers are rooted in the media getting "really nervous when you actually call out radical Islamic terrorism."