WASHINGTON — Arizona Sen. John McCain on Tuesday criticized the idea of discriminating against Syrian refugees based on religion — something backed by Republican presidential candidates Ted Cruz and Jeb Bush.

In response to a question from Mashable, McCain said: "Are we going to discriminate against children because they are not Christian? That's bizarre."

The Republican chairman of the Senate Armed Services Committee has called for a "pause" to bringing refugees from Iraq and Syria into the United States.

"We should suspend it until we are sure that nobody's going to get into the United States that can do damage to us," McCain said.

See also: Where the presidential candidates stand on Syrian refugees

"I'm not saying never take them. I don't want little children's bodies to wash up on the beach," McCain said.

Then he stopped, and interjected an aside.

"By the way — this thing about the Christians only...I view myself as a fairly religious person," he continued. "One of the tenets of my faith is that we're all God's children. Are we going to discriminate against children because they are not Christian? That's bizarre."

New Jersey Gov. Chris Christie, who is running for the Republican presidential nomination, told talk radio host Hugh Hewitt that he would accept no refugees in the United States, not even young orphans.

Some Republicans, including Bush and Cruz, have suggested that the United States should give preference to Christian refugees from Syria. During a news conference in Ankara, Turkey, Obama took a swipe at that notion, saying it was "not American."

"That's shameful," Obama said. "That's not American. It's not who we are. We don't have religious tests to our compassion."