Four children and a woman died Sunday after a boat carrying around 40 migrants from Turkey sank off the Greek island of Leros, Greece's coastguard said.

Three rescue boats and a helicopter were continuing with search operations but were being hampered by strong winds and choppy seas after the migrants' inflatable boat sank in the Mediterranean.

The teams managed to rescue 41 people, including six children and two adults who were transferred to hospital in Leros, the coastguard said.

A fisherman raised the alarm after discovering the lifeless body of the woman floating at sea, said local press reports.

Doctors were unable to revive four of the children hospitalised, Greece's ANA news agency reported. The agency said two of the four were boys aged about five with another fatality a girl of four.

The dead woman was around 20 years old, ANA reported, adding that all the migrants aboard were from Africa, including several with reduced mobility.

"Unfortunately, once again we have innocent victims who have lost their lives because of the criminal behaviour of traffickers," Greece's Merchant Navy Minister Yannis Plakiotakis said in a statement.

The number of migrants requiring rescue has risen as more attempt to reach Greece from Turkish shores on shoddy and overcrowded vessels despite the rough winter seas.

In December, a two-month-old baby died in a shipwreck off the Greek island of Lesbos.

Some 2,246 people fleeing wars and poverty are known to have lost their lives in the eastern Mediterranean since 2014, according to statistics from the International Organization for Migration (IOM).