Matthew and Grace Huang were arrested in January 2013 after the death of eight-year-old Gloria, who had been adopted from an orphanage in Ghana.
An appeals court in Doha on Sunday ruled they were not guilty and said they were free to leave.
However, the Huangs were prevented from leaving Doha yesterday after spending "10 hours" at the airport accompanied by US Ambassador Dana Shell Smith, their representative Eric Volz told AFP.
"We are waiting for the United States and the Qatari officials to resolve this mess," Volz told AFP by telephone from a Doha hotel where he and the Huangs were staying.
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A State Department spokeswoman said US officials were working with Qatari counterparts to end the situation.
"While the case was overturned, the travel ban was not yet overturned," spokeswoman Jen Psaki told reporters in Washington.
"That is... The issue at play here and one we're certainly working with all relevant folks to resolve," she said, adding there was "some paperwork that needs to be filed."
"We are deeply concerned about new delays that have prevented their departure," he said in a statement.
Kerry said he had spoken to Foreign Minister Khaled Mohammed al-Attiya, and called on Doha "to immediately implement the court's decision and permit their return to the United States without further delay".