The children's bodies were recovered by the Turkish coastguard with reports from Greece indicating that another two children may still be missing.
They were on a flimsy vessel taking at least 46 migrants from Turkey's northwestern coast to the Greek holiday island of Lesbos when the accident happened, the private Dogan news agency reported.
"It was dark, we saw the ship bearing down on us. We tried to signal with flashlights and cellphones but they did not see us," a survivor called Haseen told Greece's state news agency, ANA.
"We lost the children. We could not see them in the dark," Haseen said.
A mother and baby, who had spent at least two hours in the water, were among the survivors, according to ANA.
The Greek coastguard said it had rescued 22 people from a boat that sank off Lesbos, apparently referring to the same incident, claiming there were 48 people on board.
Greece's marine ministry said a search was underway for those missing.
Yesterday, a five-year-old Syrian girl drowned and several other refugees were reported missing after their boat also sank trying to reach Lesbos.
The latest tragedy unfolded in the same stretch of water east of the island with a helicopter deployed by EU border agency Frontex spotting the migrants in the water at around 0300 GMT, a spokeswoman for the Greek coastguard told AFP.
"Two coastguard vessels went out and rescued 22 people, including three women and a child. The survivors said there had been 46 people on board, but later this changed to 48 people," she added.
There was no information on the migrants' nationalities but the crossing from Turkey to Greece is the most popular route for Syrians, Iraqis and other people fleeing conflicts and misery in the Middle East and Asia to Europe.
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