Port-au-Prince, Haiti (CNN) -- Ten Americans held in Haiti on charges of illegally trying to take 33 children out of the country were scheduled to have their first court hearing Monday afternoon, according to the U.S. State Department.
P.J. Crowley, a department spokesman, said Monday that U.S. and Haitian authorities are "working to try to ascertain what happened [and] the motive behind these people. Clearly there are questions about procedure as to whether they had the appropriate paperwork to move the children."
The Americans were turned back Friday night as they tried to take the children across the border into the Dominican Republic. At least some of the group are members of the Central Valley Baptist Church in Meridian, Idaho.
The missionaries say they were just trying to help the children start a new life. Central Valley's senior pastor, Clint Henry, reiterated that point Monday, saying the group's intentions were "upright and pure."
"The intention was simply to go down and try to be an aid in ministering to children that had been orphaned in the quake," the pastor said. "It was our intention to be part of a new orphanage. The decision was made that we could house those children in the temporary sites."
But Haiti's prime minister said Sunday 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 added, "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. 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 an Idaho-based charity, New Life Children's Refuge, said 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 after the 7.0-magnitude earthquake January 12 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 had been detained for "alleged violations of Haitian laws related to immigration."
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.
The Americans said they believed the children were orphaned, and they were going to house them in a converted hotel in the Dominican Republic.
Georg Willeit of SOS Children's Villages, who said that Haitian police and the social ministry brought the children to his group after they were taken from the American group, said some of the children have living relatives.
"Some of them for sure are not orphans," he said. "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 Charisa Coulter, 23, who is among those arrested, told CNN affiliate KTVB on Saturday that the group members "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."
The Americans thought they had all of the necessary documents to transport the children out of the country, Coulter said, but they were stopped at the border Friday and told there was a paper missing.
"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."
CNN's Karl Penhaul, Jill Dougherty and journalist Jessica Desvarieux contributed to this report.