US embassy officials would not say whether Washington would accept hosting judicial proceedings for the Americans, but for now, the case remains in Haitian hands, PJ Crowley, a state department spokesman, said in Washington.
"Once we know all the facts, we will determine what the appropriate course is, but the judgment is really up to the Haitian government," he said.
Haitian officials say some prosecution is needed to help deter child trafficking, which many fear will flourish in the chaos caused by the devastating earthquake.
"One [9-year-old] girl was crying, and saying, 'I am not an orphan. I still have my parents.' And she thought she was going on a summer camp or a boarding school or something like that"
George Willeit, SOS Children's Village spokesman
The government and aid groups are still struggling to get food, water, shelter and basic healthcare to hundreds of thousands of survivors, and many parents are desperate to get help for their children.
The 10 Americans have not been charged, Crowley said, adding that US diplomats have had "unlimited" access to the men and women from a Southern Baptist church in the US state of Idaho.
Members of the group say they were only trying to save abandoned children.
Laura Silsby, the group's spokeswoman, said they were "just trying to do the right thing", but she conceded they had not obtained the required passports, birth certificates and adoption certificates for the children - a near impossible challenge in the post-quake mayhem.
Since their arrest on Friday near the border with the Dominican Republic, the group has been held inside two small concrete rooms in the same judicial police headquarters building where ministers have makeshift offices and give disaster response briefings.
Held in Haiti
One of the Americans, Charisa Coulter, was treated on Monday at a field hospital for either dehydration or the flu. Looking pale as she lay on a green army cot, the 24-year-old was being guarded by two Haitian police officers.
"They're treating me pretty good," she said. "I'm not concerned. I'm pretty confident that it will all work out."
|Group members said they were just "trying to do the right thing" [Reuters]
The 33 children, ranging in age from two months to 12 years, were sent to a children's home where some told aid workers they have surviving parents.
"One [9-year-old] girl was crying, and saying, 'I am not an orphan. I still have my parents.' And she thought she was going on a summer camp or a boarding school or something like that," said George Willeit, a spokesman for the SOS Children's Village.
The prime minister said some parents may have knowingly given their kids to the Americans in hopes they would reach the US – not an uncommon wish for poor families in a country that already had an estimated 380,000 orphans before the quake.
Haiti's overwhelmed government has halted all adoptions unless they were in motion before the earthquake amid fears that parentless or lost children are more vulnerable than ever to being seized and sold.
And Bellerive's personal authorisation is now required for the departure of any child.
Investigators have been trying to determine how the American church group got the children, and whether any of the traffickers that have plagued the impoverished country were involved.