Port-au-Prince, Haiti (CNN) -- Ten Americans detained and accused of child trafficking in Haiti after they allegedly tried to bus 33 children into the Dominican Republic insist their effort was an attempt to get the children to a shelter.
But Haiti's prime minister said Sunday that the group was kidnapping the children.
"From what I know until now, this is a kidnapping case," Jean-Max Bellerive told CNN. "Who is doing it -- I don't know. What are the real objectives or activities -- I don't know. But that is kidnapping and it is more serious because it's involving children," he said.
"The children certainly were not fully willing to go, because in some cases, from what I heard, they were asking for their parents, they wanted to return to their parents."
U.S. embassy officials visited the Americans over the weekend at a jail near the airport in Port-au-Prince, where they are being detained. They are being treated well and are holding on to their faith, the Americans said.
"We came into Haiti to help those that really had no other source of help," Laura Silsby, a member of the Idaho-based charity, New Life Children's Refuge, told CNN on Saturday.
"We are trusting the truth will be revealed and we are praying for that."
The group of five men and five women said they were trying to move the children to the Dominican Republic in the aftermath of the January 12 earthquake that devastated parts of Haiti, flattening the capital and killing tens of thousands. But a Haitian judge has charged the 10 with child trafficking, they said.
The U.S. Embassy in Port-au-Prince said Sunday that the Americans have been detained for "alleged violations of Haitian laws related to immigration."
"God is our provider and God gives us strength and comfort," said Carla Thompson, one group member. "We have our Bibles and we are OK."
Government approval is needed for any Haitian children to leave the country, and the group acknowledged that the children have no passports.
Jeanne Bernard-Pierre, general director for Haiti's Institute of Social Welfare, said the children will be interviewed in the coming days to determine whether they have living relatives.
Search for the missing
The group said it believed the children were orphaned, and it was going to house them in a converted hotel in the Dominican Republic.
George Willeit of SOS Children's Villages -- who said that Haitian police and the social ministry brought the children to his group -- said some of the children have living relatives.
"Some of them for sure are not orphans," he told CNN. "Immediately after she arrived here, a girl -- she might be 9 years old -- was crying loudly, 'I am not an orphan, I do have my parents, please call my parents,' " he said.
"And some of the other kids as well, they have their phone numbers, even, with them from their parents," he said. He said he believes that at least 10 are not orphans.
Mel Coulter, the father of 23-year-old Charisa Coulter, who is among those arrested, told CNN affiliate KTVB that the group thought it had all of the necessary documents to transport the children out of the earthquake-ravaged country, but apparently lacked some paperwork.
"They want to bring kids out who have no home, who have no parents, who have no hope -- and this was an attempt to give them the hope that they've lost in Haiti," he said Saturday.
The group "went down on Thursday night fully expecting that they had everything they needed, all the documentation that they needed," he said.
"When they tried to bring some of the kids out [Friday] night they were stopped at the border and [they] said that there was a paper missing," he said. "So they returned to Port-au-Prince, where they went in early [Saturday] morning to try and get the last documentation, and apparently were arrested on the spot and jailed."
He said the group wants "to do everything according to the processes that are required."
The Rev. Clint Henry, the senior pastor with Central Valley Baptist Church in Meridian, Idaho, where at least some of the group members worship, told KTVB Sunday that the church was hopeful that the group would soon be released.
"We're waiting ... and hoping and praying that that outcome will be the one that we're looking for, so the team that has been falsely charged will be vindicated, and that the whole world is going to know that we weren't here doing the kind of things we're being accused of doing," he said.
He said the accusations have prompted a number of phone calls to the church that include "obscenities, accusations about those false rumors, things that I don't care to repeat."
The children were being rescued from "one or more orphanages" that had been damaged in the quake, a statement on the church's Web site said.
Henry told CNN affiliate KIVI Saturday that the group had been planning to build an orphanage in the Dominican Republic, but that the earthquake sped up the timetable for transporting the Haitian children there.
"We weren't ready to start this yet, everything was in process," he said, and the construction on the orphanage has not yet begun.
Many of the children said they are from Fort Jacques, a town about seven miles from Port-au-Prince, according to Bernard-Pierre.
CNN's Karl Penhaul, Jill Dougherty and journalist Jessica Desvarieux contributed to this report.