BRUSSELS — A group of European Union countries has agreed to take in at least 1,600 migrant children in Greece traveling without their parents, with the first unaccompanied minors likely to find homes in Luxembourg as soon as next week, EU Home Affairs Commissioner Ylva Johansson said Friday.

There are currently over 42,000 migrants living in overcrowded camps in the Greek islands, including about 5,500 unaccompanied minors. According to the police agency Europol around 10% of them are younger than 14.

Finland, France, Germany, Luxembourg and Portugal have offered to take them in, and Johansson said that at least two other countries expressed an interest in getting involved during a meeting Friday of EU interior ministers. She did not name them.

Earlier this week, Johansson said that migrant children traveling alone “face violence, abuse and exploitation. Many of them just disappear from the asylum and reception centers and we don’t know where they are. I am afraid that many of them fall into the hands of criminals.”

She said Friday Greek authorities have told her that quite a few are going to school each day, although some are dropping out, several choosing to try vocational training instead. She said that “a lot are living in quite OK conditions,” but some fall off the radar.

Greece requested help to care for lone child migrants last September. The EU’s executive commission also asked for assistance from member countries but none was forthcoming. Johansson suggested that tensions between Greece and Turkey over migrants might have spurred countries into action.