The Turkish coastguard recovered the bodies of the children, including a baby, and were still looking for two other migrants reported missing, the official Anatolia news agency said.
The inflatable dinghy sank in strong winds and high waves near the town of Cesme in western Izmir province, Anatolia said. It was apparently heading for the Greek island of Chios.
Eight other migrants, all wearing life jackets, were rescued, Dogan news agency said.
In a separate incident, the body of Sajida Ali, a five-year-old migrant girl, washed up on a beach in Cesme on Monday, Dogan said.
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Turkey hosts more than two million refugees from the Syrian conflict and is the main launching point for migrants coming to Europe, via Greece.
Turkish authorities have stepped up efforts to stop migrants from leaving for Greece after Turkey and the European Union reached a deal to stem the flow of refugees into Europe on November 29.
The authorities last week rounded up 3,000 migrants as they were preparing to make their way to the Greek island of Lesbos from the northwestern town of Ayvacik in Canakkale province.