There were widespread fears that child traffickers would take advantage of the chaos in Haiti following the quake to pick up youngsters and sell them abroad.
Clinton stressed that he was not in Haiti to intervene in the case, but he expressed his hopes that Washington and Port-au-Prince would work together to resolve the situation.
"I think what's important now is that the government of Haiti and the government of the United States to get together and go through this because the government of Haiti, as I understand it, is not looking for a fight," he said.
"They just want to protect children," he said.
"I know that the [US] state department and government have had these discussions," he said.
His remarks came after his wife, US secretary of state Hillary Clinton, said that the US ambassador to Haiti was keeping in touch with Haitian officials over the case.
"Obviously, this is a matter for the Haitian judicial system," she said.
The missionaries, from an Idaho-based Baptist church, were questioned individually on Friday by Bernard Sainvil, the investigating judge, at the offices of the prosecutor in the city.
Officials said the judge would continue his investigation on Monday and Tuesday, before making a decision on whether to release the 10 or proceed with the case against them.
Haiti 'still has laws'
The administration of Rene Preval, the Haitian president, has defended its decision to detain and charge the Americans.
"It is true the country has been brought to its knees by the earthquake, but we still have laws"
Haitian justice minister
"It is true the country has been brought to its knees by the earthquake, but we still have laws," Paul Denis, the justice minister, said.
"In any case, whoever violates the law has to be sanctioned, whether the violator is a US or European citizen, or someone else."
Preval met Clinton on Friday, but the former US president said that the meeting focused on his mission to help the relief and rebuilding effort in the country after more than 200,000 people were killed and one million made homeless.
During his visit to Port-au-Prince, he apologised for delays in getting aid to the survivors.
"I'm sorry it's taken this long," Clinton said. "I'm trying to get to what the bottlenecks are, part of it is just shipping the volume of food in here that is necessary."
In the immediate aftermath of the disaster, rescue operators struggled to get aid out to earthquake victims and many aid groups called for greater co-ordination.
Jonah Hull, Al Jazeera's correspondent in Port-au-Prince, said that Clinton's mission was larger than simply addressing the basic needs of the people struggling to get shelter, food and water.
|Clinton has been appointed by the UN to lead Haiti's reconstruction efforts [AFP]
"He will also need to look, more importantly, towards the long-term recovery of this country - rebuilding infrastructure, in many cases from the ground up," he said.
"And also he will need to rebuild the economy, working with international partners to make sure markets are open to Haitian produce rather than subsidised international imports flooding into this country.
"Mr Clinton's role is not to be directly involved in the distribution of aid, his role is to co-ordinate the international partners, the donors, the money.
"He has got to get the money flowing, he has got to keep in flowing and he has got to make sure it is going in the right direction to rebuild this country."
Last week, Clinton urged corporate leaders at the World Economic Forum in Davosto use the Haiti catastrophe as an opportunity to lift the devastated nation out of generations of poverty.