The United States should not "punish the victims of ISIS for the sins of ISIS" by stopping the resettlement of Syrian refugees following the horrific terrorist attacks in Paris on Friday.

The plea was made by two of America's largest and most influential religious groups—the U.S. Conference of Catholic Bishops and the National Association of Evangelicals (NAE) — after U.S. House Speaker Paul Ryan called for a "pause" in the U.S. programme for accepting Syrian refugees, CNN reported.

At least 27 U.S. state governors have also said they will not welcome the refugees amid fears that some of them could be covert terrorists sent by the Islamic State (ISIS) to wreak havoc on America.

"Of course we want to keep terrorists out of our country, but let's not punish the victims of ISIS for the sins of ISIS," Pastor Leith Anderson, NAE president, said on Tuesday.

"I am disturbed ... by calls from both federal and state officials for an end to the resettlement of Syrian refugees in the United States," Bishop Eusebio Elizondo, Chairman of the Catholic bishops' committee on migration, said on Tuesday.

"These refugees are fleeing terror themselves—violence like we have witnessed in Paris. They are extremely vulnerable families, women, and children who are fleeing for their lives. We cannot and should not blame them for the actions of a terrorist organisation."

The joint appeal made by the evangelical and Catholic church groups—which comprise 45,000 churches—put several Republican presidential candidates in a dilemma since what they are demanding is the opposite of what their churches want. Sen. Marco Rubio, New Jersey Gov. Chris Christie, and former Miami Governor Jeb Bush are Catholic. Texas Sen. Ted Cruz and former Arkansas Governor Mike Huckabee are evangelicals.

Cruz later tempered his call for an end to U.S. resettlement of Syrian refugees by saying that the U.S. should "focus" on getting Christian refugees who are victims of persecution, and not Muslims.

The Catholic and evangelical church leaders said the fears that terrorists could infiltrate the ranks of the refugees and sow mayhem in the U.S. are unfounded, the Catholic and evangelical leaders said.

The U.S. has a "strong track record" for screening refugee applicants, Anderson said.

Elizondo echoed that thought, noting that refugees must pass security checks and multiple interviews before entering the United States.

"Instead of using this tragedy to scapegoat all refugees," the bishop said, "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."

But other religious leaders have a different view on the matter. Rev. Franklin Graham, the son of famed evangelist Billy Graham, in a message he posted on his Facebook page on November 14 said: "We cannot allow Muslim immigrants to come across our borders unchecked while we are fighting this war on terror. If we continue to allow Muslim immigration, we'll see much more of what happened in Paris—it's on our doorstep."