The UN says the group of 35 Syrians and three Palestinians had been stranded for several days in a restricted military zone.
Greek authorities have confirmed that a five-year-old has died after she was discovered trapped on an islet with a group of migrants.
A total of 38 people were located by Greek police in the border river of Evros on Monday evening.
Athens says they were located in a boat "outside Greek territory" around four kilometres away from the islet, which is known as Meriç in Turkish.
The United Nations says that the group -- 35 Syrian nationals and three Palestinians -- had been stranded for several days in the restricted military zone.
The Greek Minister of Migration has accused Turkey of forcing the migrants to cross the border "under the threat of violence".
"They forced them to head for Greece and the European Union," Notis Mitarachi in a statement on Tuesday after visiting the scene.
He added that Greek authorities are working with the International Committee of the Red Cross (IRC) to find the body of the five-year-old girl "so that she can be buried with dignity by her family". NGOs say she died after being stung by a scorpion.
A pregnant woman was also found among the group of migrants and has been hospitalised. On Saturday, the UN High Commissioner for Refugees had called for "urgent measures" to save them.
Greece initially said they had carried out "multiple searches" and said that Ankara was responsible for finding the stranded migrants in their territory.
The head of the Greek Council for Refugees has claimed that the migrants feared physical abuse if they re-entered Greece.
Athens has been repeatedly accused of illegally pushing back asylum-seekers to Turkey on its land and sea border in the Aegean. Greece has always denied these accusations.
"This latest situation at the Evros border highlights the brutality of pushbacks, which we know are taking place at borders across Europe," said Dimitra Kalogeropoulou, IRC Greece Director.