In a joint statement the International Organization for Migration, the UN refugee agency, and the UN Children’s Fund (UNICEF) welcomed the relocations as "an encouraging start".
“The importance of this crucial initiative is amplified now due to the challenges we are all facing from COVID-19. Relocation of vulnerable children, especially at a time of heightened hardship, sends a strong message of European solidarity and we hope to see this expand soon,” IOM regional director Ola Henrikson said.
Greece, which is sheltering more than 5,000 unaccompanied migrant children, has been repeatedly criticised for failing to provide decent conditions for the youngsters in police stations and camps.
"As #COVID19 is testing our humanity, it is heart-warming that relocations of unaccompanied children from Greece have started today (with) Luxembourg," Council of Europe Commissioner for Human Rights Dunja Mijatovic tweeted.
"Many more are stranded there and I urge all other Council of Europe states to quickly follow suit and live up to our core values of solidarity and dignity."
Human Rights Watch (HRW) this week called on Greece to release the more than 300 unaccompanied children held in "unhygienic police cells and detention centres".
"Keeping children locked up in filthy police cells was always wrong, but now it also exposes them to the risk of COVID-19 infection," HRW Greece researcher Eva Cosse said in a statement, referring to the coronavirus pandemic sweeping the world.
There have so far been two outbreaks of the virus in camps on the Greek mainland, forcing officials to lock down both facilities and resist pressure to move asylum seekers to the mainland.
Some 100,000 asylum seekers are currently staying in Greece, most of them in camps, hotel rooms and flats.
The camps on islands near Turkey suffer the worst overcrowding - with more than 36,000 people in sites built for 6,100.
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