NOGALES, Mexico — Dominican Sister Donna Markham, president and CEO of Catholic Charities USA, grew emotional talking about the harrowing stories she heard from immigrants about the life they left behind to seek refuge in the United States.

“The suffering they are going through is unimaginable,” she said after listening to stories from families waiting to apply for asylum at the international border at Nogales in the Mexican state of Sonora.

Sister Markham, who recently completed a tour of a detention facility for children in McAllen, Texas, said she wanted to visit Nogales to get the whole story behind the current public debate over immigration.

“Their stories,” she said, pausing to compose herself. “They are running for their lives. Literally, they left at gunpoint.”

She was joined July 11 at the Nogales Port of Entry by Jesuit Father Sean Carroll, executive director of the Kino Border Initiative, an organization that assists mostly families who have been sent back to Mexico following deportation proceedings.

With the large influx of refugees seeking to enter the U.S., Father Carroll, along with other religious-based and nonprofit agencies in Nogales, Ariz., have set up temporary shelters and a check-in system for families seeking to enter the U.S. and to apply for asylum.

The first family Sister Markham met included 11 members, four of whom were young children. They left the Mexican state of Guerrero, one of the poorest and most dangerous areas in the country.

Father Carroll interpreted their story, explaining how their lives had been threatened by a local political party during the recent presidential election. At the border, their biggest fear is that the father and uncle would be detained, the children taken from them, and the women deported. Knowing that risk, they waited anyway because “they were threatened with death” in their hometown, Sister Markham said.

While such conditions might easily fall into the classic example of political asylum, Peg Harmon, who is executive director of Catholic Community Services in the Diocese of Tucson and has been a Catholic Charities USA board member, acknowledged that under the current vetting system, there were no guarantees.

Following her meeting with the families, Sister Markham said there were two things she hoped to accomplish when she returns to her organization’s national headquarters outside Washington.

“We need to call all believers to prayer, and we have to educate people who don’t have the opportunity to come here,” she said.