The attacks have led several GOP governors, including Asa Hutchinson of Arkansas and Greg Abbott of Texas, to vocally oppose the relocation of Syrian refugees into their states.
Some GOP leaders, including presidential candidates Jeb Bush and Sen. Ted Cruz, have said that only Christian refugees should receive any U.S. assistance. And Donald Trump told CNBC on Monday that letting them in "would be one of the great Trojan horses."
At the G-20 meeting in Turkey, Obama said: "When I hear folks say that we should just admit the Christians but not the Muslims, when I hear political leaders suggesting there will be a religious test for which a person fleeing from a war-torn country is admitted ... that's shameful. That's not American."
He added: "I had a lot of disagreements with George W. Bush on policy, but I was very proud after 9/11 when he was adamant and clear that this is not a war on Islam. And the notion that some of those who have taken on leadership within his party would ignore all of that is not who we are," Obama said. "On this they should follow his example."