Florida Gov. Jeb Bush, also a GOP presidential candidate, over the weekend went so far as to call on the U.S. to grant asylum only to Syrian Christians. And Republican lawmakers on Monday introduced a bill that will attempt to block funding for the country’s refugee resettlement program.

House Speaker Paul Ryan clarified Wednesday that the bill, which will be up for a vote later this week, will not limit Syrian refugees admitted to the U.S. based on their religions, The Associated Press reported.

But Christian charities and groups in the U.S. that work with refugees have balked at Republicans’ statements and urged support for Syrian refugees of all faiths.

Syria's deadly civil war has stretched into a fifth year, with some 250,000 people killed in the conflict, according to the United Nations. The fighting spurred an estimated 4.2 million Syrians to flee the country. While the majority reside in camps in neighboring countries, including Turkey and Jordan, thousands have landed on European shores, sparking a resettlement crisis.

“We think that their position is very misguided,” Mitzi Schroeder, director of policy for Jesuit Refugee Service/USA, told Al Jazeera. “We have resettled 3 million refugees in the U.S. since 1975; they have not been a source of terrorist concern.”

Obama on Wednesday lambasted the GOP leaders’ statements as offensive and “based on hysteria.” His administration has said it will bring 10,000 Syrian refugees into the country by the end of 2016, adding to the scant 2,058 of them who have arrived in the U.S. since January 2014.

Most of the Syrian refugees, Schroeder said, have endured incredible hardships. “We’re talking about widows, we’re talking about trauma survivors, we’re talking about the elderly,” she said. “We really feel strongly that the [resettlement] decisions should be made on need, on persecution, on suffering, and not on any other criteria,” she added.

According to Matthew Soerens, spokesman for World Relief, a non-profit Christian group that is one of the nine national organizations authorized by the federal government to help resettle refugees in the U.S., the vetting of refugees by the Department of State is rigorous.

The process takes at least 18 months, often more. “Obviously security is going to be the first priority,” Soerens told Al Jazeera.

He added that despite any potential involvement of Syrian nationals in last week’s attacks in Paris, “We don’t see that as a reason to stop welcoming carefully vetted refugees into the U.S. who are fleeing, sadly, the persecution and terror that so many Parisians have experienced” in recent days.

Bishop Eusebio Elizondo, who chairs the committee on migration for the United States Conference of Catholic Bishops' (USCCB), expressed dismay on Tuesday that federal and state officials had called on the U.S. to end the resettlement of Syrian refugees, and pointed out that Syrians were fleeing the very same violence that was inflicted upon Parisians.

“Instead of using this tragedy to scapegoat all refugees, I call upon our public officials to work together to end the Syrian conflict peacefully so the close to 4 million Syrian refugees can return to their country and rebuild their homes,” Elizondo said in a statement posted on the USCCB website.

Religious groups were adamant that not only should refugees not be turned away, but they should also not be screened on the basis of their faith.

“We do not feel that Christian refugees should get preference,” Schroeder said, though she added that if refugees are being persecuted on the basis of religion, then those refugees deserve consideration by the U.S., “according to international law.”

She added that the millions of refugees in the Middle East and Europe also desperately need food, medicine, shelter and access to education. “We also need to increase our assistance response as well, because most of the people in this group who need help might never have access to resettlement,” she said.