At least 12 Syrian migrants trying to reach Greece have drowned when two boats sank in Turkish waters.

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As the Turkish coastguard and media announced the news, an image of a toddler's lifeless body washed ashore sparked horrified reactions on social media.

The coastguard said in a statement two boats had sunk after separately setting off from Turkey's Bodrum peninsula for the Greek Aegean island of Kos early on Wednesday.

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The corpses of 12 migrants, including five children and one woman, were found and 15 people were rescued, with some surviving after reaching the shore in life jackets.

The coastguard, backed by helicopters, was continuing its search for three people still missing, the statement said.

The Dogan news agency published an image of a corpse of a little boy wearing a red T-shirt lying face-down on the beach near Bodrum, one of Turkey's prime tourist resorts.

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The hashtag #KiyiyaVuranInsanlik ("Humanity washed ashore") made it to Twitter's top world trending topics after the image was widely shared.

Dogan said that most of the refugees were from the Syrian Kurdish town of Kobane who fled to Turkey last year to escape violence by Islamic State extremists.

Over the last week there's been a dramatic spike in the numbers of migrants - mainly from Syria, Afghanistan, Pakistan and Africa - seeking to leave Turkey by sea for Greece in the hope of finding new lives in the European Union.

The Turkish government said this week that the coastguard had rescued over 42,000 migrants in the Aegean Sea in the first five months of 2015 and more than 2160 in the last week alone.

A coastguard official told AFP around 100 people had been rescued by Turkish rescue teams overnight on Tuesday to Wednesday as they tried to reach the island of Kos.

The United Nations refugee agency UNHCR said more than 2500 people have died trying to cross the Mediterranean so far this year.

Migrants, many of whom have paid over $US1000 to smugglers for the risky passage, are taking advantage of the calm summer weather which makes this the best time for the crossing.