But she said that screening procedures had improved since then. She also said that the vast majority of the three million refugees brought to the United States since 1975 — including 19,000 Iraqis who were resettled in the 2014 fiscal year — have integrated peacefully. (The United States has taken in about 1,500 refugees from Syria since the start of the conflict there more than four years ago.)

Ms. Richard said many Americans had long supported refugee resettlement programs. “It’s an American tradition, and a lot of Americans get that,” she said. In many parts of the country, including South Carolina, the Syrian crisis has elicited calls for compassion and offers of help: On Sept. 13, hundreds of people gathered in University City, a suburb of St. Louis, to ask the federal government to accept “as many Syrian refugees as possible” in the area, according to the St. Louis chapter of the Council on American-Islamic Relations.

This week, the mayors of 18 American cities, including Bill de Blasio of New York and Eric Garcetti of Los Angeles, sent a letter to President Obama urging him “to increase still further the number of Syrian refugees the United States will accept for resettlement.” The mayors asserted that the United States had a “robust screening and background check” system in place for refugees, who, they said, “have helped build our economies, enliven our arts and culture, and enrich our neighborhoods.”

But even before the Syrian crisis dominated headlines worldwide, resettlement agencies had noted a rise in anti-refugee sentiment in parts of the United States, said Melanie Nezer, vice president of policy and advocacy at HIAS, a Jewish nonprofit that works with refugees. In the last two decades, they have increasingly placed people in smaller communities to try to avoid the high cost of living in traditional immigrant magnets like New York and Los Angeles. At the same time, unemployment and tight budgets have prompted some local governments to fight the placement of refugees.

In South Carolina, a number of influential Upstate religious leaders have embraced the refugee program. The Rev. D.J. Horton, senior pastor of Anderson Mill Road Baptist Church, said dozens from his flock of 2,300 had already completed refugee support training. “It’s very hard to read your Bible, especially your New Testament, and refuse refuge to people who are vulnerable,” he said.

Mr. Lee said World Relief has proposed to the State Department resettling as many as 116 refugees in the Upstate region in the next year. He did not rule out the possibility that Syrians might be resettled in the area in the future. For now, he said, his group had resettled just one Muslim family of four, from Iraq, and a former Iraqi translator for United States security companies who has renounced his religion.

The former translator met with a reporter on Monday and asked that his name not be used, for fear of attracting attention from anti-refugee activists. He said his reception in the United States had been warm, but he had been careful not to mention he is an Iraqi: Among Americans, he said, “Suicider, killer — this is the stereotype of Iraq.”