The children are in the Panorama Park Hotel in Icmiler near the famous resort of Marmaris.
The source said the situation was not unusual for Turkish resorts, although similar incidents had rarely happened to large groups. The Turkish authorities as a rule look for compromise in such cases, the source added.
When the group gathered in the hotel lobby to go to the airport, the police came and gathered everyone in the hotel's conference hall, one of the children said over the phone.
"The hotel manager asked us to call our parents to tell them to transfer money that, according to him, the travel agency had not paid for the accommodation," said 18-year-old Albina.
The hotel management has confirmed that it is keeping 118 children on its premises, because the tourist firm did not pay.
When reached by telephone, Spectrum, the Moscow-based travel agent that organized the trip, gave assurances that everything would be "all right".
The children were supposed to take a flight from Turkey to Moscow at 7 p.m. local time (4 p.m. GMT).
Russian diplomats said they were trying to solve the problem.