Barack Obama launched a fierce attack on Republican candidates who argued that Muslim refugees must be kept out of America on Monday, saying: “We do not have religious tests for our compassion.”

The proposals that Christians should be prioritized as refugees from Syria were shameful and un-American, the president told a G20 press conference in southern Turkey.

“When I hear political leaders suggesting that there should be a religious test for admitting which person fleeing which country,” Obama said, “when some of these folks themselves come from other countries, that’s shameful.

“That’s not America. That’s not who we are. We don’t have religious tests to our compassion.”

Republicans, including former Florida governor Jeb Bush and Texas senator Ted Cruz, called at the weekend for Christians to be given priority in the Syrian refugee crisis, following the attacks in Paris on Friday that killed 129 people and were claimed by the Islamic State group.

Obama did not name any candidates in his appearance on Monday in Turkey.

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“We should focus our efforts as it relates to refugees on the Christians that are being slaughtered,” Bush, the brother of former president George W Bush and the son of former president George HW Bush, said on Sunday in an appearance on CNN. “I think our focus ought to be on the Christians who have no place in Syria any more.”

“There is no meaningful risk of Christians committing acts of terror,” Cruz, whose father arrived in the United States via Canada as a refugee from Cuba, said in a speech in South Carolina on Sunday. “But it is precisely the Obama administration’s unwillingness to recognize that or ask those questions that makes them so unable to fight this enemy. Because they pretend as if there is no religious aspect to this.”

Addressing a ballroom full of the international press in Turkey, Obama argued sharply that there should be no religious aspect to US policy on admitting refugees.

“I think it is very important for us right now, particularly those who are in leadership, particularly those who have a platform and can be heard, not to fall into that trap,” Obama said. “Not to feed that dark impulse inside of us.

“I have a lot of disagreements with George W Bush on policy. But I was very proud after 9/11, when he was very adamant and clear that this is not a war on Islam.

“And the notion that some of those who have taken on leadership in his party would ignore all of that – that’s not who we are. On this, they should follow his example. It’s the right one. It’s the right impulse, it’s the better impulse.”

Florida senator and presidential hopeful Marco Rubio, whose parents emigrated from Cuba, also departed from George W Bush’s framework in a video released by his campaign after the Paris attacks. “This is not a grievance-based conflict,” Rubio said. “This is a clash of civilizations. And either they win, or we win.”

Obama implied that Republicans had lost sight of Christian teaching, by recalling an address to a joint session of Congress earlier this year by Pope Francis.

“When Pope Francis came to visit … he didn’t just speak about Christians who were being persecuted,” Obama said. “He said protect people who are vulnerable.

“The people who are fleeing Syria are the most harmed by terrorists, they are the most vulnerable as a consequence of civil war and strife.”

In a news conference in Nevada following the president’s remarks, Republican presidential hopeful Ben Carson said that Syrian refugees being resettled in the United States should be closely monitored.

“Congress, I think, should defund all the programs that allow these people to be brought here immediately, today,” Carson added, according to Reuters.

Praising the German chancellor, Angela Merkel, for showing compassion and leadership on the issue of refugees, Obama urged the world to remember the biggest victims of violence in Syria were Muslims.

Obama said: “The people who are fleeing Syria are the most harmed by terrorism. They are the most vulnerable as a consequence of civil war and strife. They are parents. They are children. They are orphans and it is very important … that we do not close our hearts to these victims of such violence and somehow start equating the issue of refugees with the issue of terrorism.”

In September, Obama directed his administration to prepare to accept 10,000 new refugees from Syria in the next fiscal year. An estimated half a million refugees from the Syrian conflict have arrived in Europe this year, about 51% of them women and children.

“It is good to remember that the United States does not have a religious test, and we are a nation of many people of many faiths,” Obama concluded. “Those are the universal values that we stand for.”