A smuggling boat has sunk off a Greek island, killing at least 16 migrants including children.

A search and rescue operation is under way to find two others believed missing.

The wooden boat was believed to have been carrying around 21 people when it sank for reasons that were not immediately clear off the coast of the eastern Aegean island of Agathonisi, the Greek coast guard said.

Three people – two women and one man – managed to swim to the island and alert authorities.

A massive search operation involving aircraft, the Greek navy and coast guard and a vessel from the European border agency Frontex is under way.

A coast guard spokeswoman said the recovered bodies had not been identified yet and they included six children.

Despite a two-year deal between the European Union and Turkey designed to stop migrants and refugees from pouring into Europe from the Turkish coast to nearby Greek islands, dozens and sometimes hundreds of people still make the journey each week.

Most cross in rickety inflatable boats or other unseaworthy vessels.

The UN Refugee Agency released a statement saying it is “deeply saddened” at the sinking.

“Some 4,000 people, mainly women and children from Syria, Iraq and Afghanistan, have arrived by sea to Greece so far this year. Today’s tragic incident is the first shipwreck in the Aegean of 2018, but some 500 refugees and migrants lost their lives or went missing in the Greek Aegean Sea over the past two years,” it said.

The agency said “renewed efforts are needed to combat smuggling and trafficking and to strengthen safe alternatives to the perilous sea journeys”.

Demonstrators marched through central Athens protesting against the EU-Turkey migrant deal, whose second anniversary falls on Sunday.

Migrants who live in Greece during a rally in Athens against the EU-Turkey deal blocking mass migration into Europe (Yorgos Karahalis/AP)
Migrants who live in Greece protest in Athens against the EU-Turkey deal blocking mass migration into Europe (Yorgos Karahalis/AP)

About 2,000 protesters ended the march outside EU offices, decrying Europe’s closed borders.

“The latest tragedy at Agathonisi underlines in the worst and saddest way that human life cannot depend on the interests of smugglers, nor on the policies of states,” Greek migration minister Dimitris Vitsas said.

He said the solution to the problem is providing safe procedures for refugees and migrants while also cracking down on smuggling rings.