It came as a judge refused to grant the 10 Americans bail and returned them to prison ahead of their case.
The 10 men and women were denied bail and returned to a Haiti prison
Speaking to CBS News, the leader of the missionary group, Laura Silsby, said: "We have in no way wanted to disrespect the Haitian government.
"We have tried our best to comply with all they have asked us to do. We have not in any way trafficked or kidnapped children.
Laura Silsby, US missionary leader
They came with armed guard and took us to the police station for interrogation and held us on charges - on false charges.
"We came here out of our love in our hearts for these children and have done our best to help them.
"One we were asked at the border to provide an additional piece of paperwork for the Haitian government, we willingly complied.
"I was willing to come back the very next morning at 6am to complete it and the children were going to remain there until I returned.
"But instead they came with armed guard and took us to the police station for interrogation and held us on charges - on false charges."
At their court hearing, the lawyer representing the group told reporters he asked the judge to grant the detainees "provisional release," a type of bail without money posted.
Edwin Coq said they should be allowed to leave Haiti until their trial, a date for which has yet to be set.
But the judge rejected the request and the accused were driven back to jail ahead of a further hearing scheduled for next week.
An investigating judge charged the Americans on Thursday with kidnapping for trying to take 33 children across the border into the Dominican Republic without documentation.
The Baptist group, most of whose members are from two Idaho churches, insisted they were rescuing abandoned children and orphans after the quake.
But at least 22 of the children, ranging in age from two to 12, have parents.
Some of the parents said they gave them up willingly because the missionaries promised the youngsters a better life.
Each of the missionaries is charged with one count of kidnapping, which carries a sentence of five to 15 years in prison.
They are also accused of criminal association, which is punishable by three to nine years.