Crowley said the State Department has been given "unlimited" access to the jailed missionaries, and that they appear to be treated well.
"I can assure you that the intent of our group going down there had absolutely nothing to do with kidnapping and everything to do with helping a desperate situation in Haiti," the Rev. Clint Henry, from the Central Valley Baptist Church in Meridian, Idaho, said on "Good Morning America.".
The 10 Baptist missionaries said they were attempting to bring the Haitian children to an orphanage across the border in the Dominican Republic when they were arrested Friday night at a border crossing.
"They were arrested on the border with children that were not theirs, and that they had no papers for," Haitian Prime Minister Jean-Max Bellerive told ABC News. "For me, it's not Americans that were arrested, it was kidnappers that were arrested."
Henry said he spoke to the missionaries Friday night before they tried to cross the border, and they told him there was some confusion over what paperwork they needed to bring the children into the Dominican Republic.
"[They] indicated to me they were doing everything they could to work with the authorities to have the right paperwork and that became one of their frustrations -- not understanding everything they needed to have," Henry said.
Some of the children were apparently not orphans, said George Willeit of SOS Children's Villages, an nongovernmental international group.
"We already know that some of these children still have parents because an elder girl, maybe 8 or 9 years old, told us crying, 'I am not an orphan. I do have my parents. I thought I was going to boarding school or to a summer camp,'" Willeit said.
Henry said that the situation was "as much of a surprise to me as anyone else."
"The last that I knew is that we were working with a pastor who was dealing with an orphanage there, and I don't know any other information beyond that," Henry said.
The Americans are being held in a police station near the airport at Port-au-Prince, the Haitian capital, and have been visited by U.S. officials, according to a statement by the U.S. Embassy in Haiti.
"We came here simply to help these children, and we went to the border based on the approval of the Dominican government to take the children into the Dominican Republic and the pastor entrusting these precious children to our care because his orphanage collapsed and his churches collapsed, and he had nowhere for these children to go," the group's spokeswoman, Laura Silsby, said.
"In this chaos the government is in right now, we were just trying to do the right thing," she said.
When asked about the charges against them, several in the group simply responded to ABC News, "Philippians 1." The Bible's first chapter of Philippians chronicles the apostle Paul's time in prison for preaching the gospel.
ABC News' Kirit Radia, Ayana Harry and Steve Portnoy contributed to this report.