* Greek coast guard searching for 38 migrants off Lesbos

* Seven drown, including four children, 242 rescued off Lesbos

* Another 123 rescued in other incidents, baby missing near Samos

By Michele Kambas and Angeliki Koutantou

ATHENS, Oct 29 (Reuters) - Four children, two men and one woman drowned and 38 migrants were missing after their wooden boat sank north of the Greek island of Lesbos, the coast guard said on Thursday, as an extensive search operation continued for a second day.

The coast guard rescued 242 people off Lesbos on Wednesday in what was thought to be the largest maritime disaster off Greece in terms of numbers involved since a massive refugee influx began this year. The search went on overnight.

Four coast guard vessels were deployed on Thursday, assisted by fishing boats. Three helicopters were hovering above the sea.

Lesbos, which lies less than 10 km (6 miles) from the Turkish coast in the north Aegean Sea, has been a primary gateway for thousands of migrants entering the European Union's outermost border.

Another 123 people were rescued off the islands of Samos and and Agathonisi, and in another incident off Lesbos. In total, 15 people drowned on Wednesday including ten children, the coast guard said. A baby has been missing for more than 12 hours.

Doctors and volunteers on Lesbos made desperate efforts to help a baby breathe, TV footage showed. Some of the survivors were sheltered in a chapel, a Reuters witness said.

"We will really support Greece," German Foreign Minister Frank-Walter Steinmeier told a Greek newspaper before an official visit to Athens on Thursday, the latest in a series of visits by EU officials to the crisis-hit country.

"It's clear that Greece - which is trying to get back on its feet right now - is feeling this influx as a particular burden."

More than 500,000 refugees and migrants have entered Greece through its outlying islands since January, transiting on to central and northern Europe in what has become the biggest humanitarian crisis on the continent in two decades.

Inflows have increased as refugees try to beat the onset of winter, crossing the narrow sea passages between Turkey and Greece in small overcrowded boats.

EU leaders have agreed to boost cooperation and provide UN-aided housing for 100,000 people, half of them in Greece. The EU is expected to cover costs for accommodation for 20,000 in leased apartments in addition to temporary camps for 30,000 people.

Relocation of migrants from Greece to other EU states could take up to two months, Migration Minister Ioannis Mouzalas said, adding that the risk of thousands of refugees being trapped in Greece from possible border closures was a remote case. "That's a tragic scenario ... but I consider the chances of that very small," he said.

(Writing by Renee Maltezou; Editing by Richard Balmforth) ((renee.maltezou@thomsonreuters.com; +30 210 3376439; Reuters Messaging: renee.maltezou.reuters.com@reuters.net))