GOP presidential candidate Donald Trump speaks to guests during a rally at Des Moines Area Community College Newton Campus, Nov. 19, 2015, in Newton, Iowa. Scott Olson/Getty Images

UPDATE: 2:10 p.m. EST -- Donald Trump responded Friday to criticism of his comments suggesting that Muslims should be monitored in the United States. He tweeted saying that the mention of a database had come from a reporter, and was not originally his idea.

Other Republican presidential candidates joined in Friday to criticize Trump's remarks, although none as strongly as former Florida Gov. Jeb Bush had Friday morning. Ben Carson, Texas Sen. Ted Cruz and Ohio Gov. John Kasich all rejected Trump's support for requiring Muslims to register with the government.

Cruz said he was "a big fan of Donald Trump's but I'm not a fan of government registries of American citizens," according to Politico. "The First Amendment protects religious liberty, I've spent the past several decades defending religious liberty," he added.

UPDATE: 1:06 p.m. EST -- Vermont Sen. Bernie Sanders, Clinton's main opponent for the Democratic presidential nomination, issued his own statement on Donald Trump's remarks about Muslims Friday afternoon. "This is an outrageous and bigoted statement. Mr. Trump should be ashamed of himself. We will not destroy ISIS by undermining the Constitution and our religious freedoms," Sanders' statement read.

Original story:

Hillary Clinton and Jeb Bush both slammed Republican presidential front-runner Donald Trump Friday for saying he would “absolutely” require Muslims in the United States to register in a database. The New York billionaire said earlier this week he was open to the idea of a database, and Thursday night he told NBC News, “I would certainly implement that -- absolutely.”

Trump’s comments quickly drew criticism on social media, with many comparing his suggestion to the Nazis forcing Jews to register during the Holocaust, but no other presidential candidates immediately weighed in Thursday night. Friday morning, Bush addressed the issue on CNBC’s “Squawk Box” and Clinton took to Twitter to express her disapproval.

Bush, the former governor of Florida, told CNBC he disagreed with Trump and called his idea “just wrong.”

"It’s not a question of toughness. It’s manipulating people's angst and their fears. That’s not strength. That’s weakness," Bush said Friday. "And look, campaigns are important, for sure. We’re electing a president, but there are things that are important as it relates to the values that we have as a country that make us special and unique, and we should not and we will never abandon them in the pursuit of this fight. We don't have to. We can protect our freedoms here."

When Trump was discussing his idea with NBC News, the reporter asked him how his database would be different from the situation Jews experienced in Nazi Germany, and Trump responded, “You tell me,” repeating the phrase multiple times.

In the week after last Friday’s deadly terror attacks in Paris, Trump has said he would consider closing some mosques to help fight the threat of terrorism.

"Nobody wants to shut down religion institutions or anything, but you understand it," Trump told Fox News' Sean Hannity on Tuesday. "A lot of people understand it. We’re going to have no choice."

Trump, along with Ben Carson, the other top Republican presidential candidate, has drawn the ire of Muslim groups this week for inflammatory remarks about Syrian refugees coming to the United States. Many politicians have raised security concerns about accepting Muslim refugees after the attacks in Paris, and the U.S. House voted Thursday to restrict the number of refugees coming from Syria and Iraq. As of Friday, Trump was holding his lead in the polls with 24.6 percent, according to the Real Clear Politics average of national polls, followed by Carson at 21.8 percent.