Germany says 10 European countries have agreed to take 400 unaccounted minors, who fled Greece’s largest migrant camp due to the blaze.
Most will go to Germany and France, Interior Minister Horst Seehofer told reporters on Friday.
About 13,000 people were living in squalor at Moria Camp in Lesbos.
The family is sleeping in the fields and on the streets after fleeing from the blast on Wednesday, as authorities struggle to find accommodation for them.
Near the ruins of Moria, island residents blocked roads to prevent them from distributing aid, saying they were against the construction of new tents.
But the Greek army later used helicopters to reach the site and began to install replacement dwellings.
After visiting the area, the European Commission vice-chairman Margaritas Cinicas announced that the devastated camp would be replaced by a modern facility at the same location.
The Moriya camp was initially designed to house 3,000 migrants. People from 70 countries took refuge there, most of them from Afghanistan.
Place of incident
By Bethany Bell, BBC News, Lesbos
Migrants from the burnt Moriya camp are protesting in front of police barricades that prevent them from moving to other parts of the island.
Singing and beating plastic bottles, they up and down a section of the coastal road, calling for the right to leave Lesbos.
One person embossed a large piece of cardboard with the message: “We don’t want food, we want freedom.” Another banner read: “Moriah kills all lives”.
Many local Greeks also want migrants to leave the island.
They strongly oppose the plans to rebuild a temporary camp. The sanitation situation is critical. There is little running water, and it is difficult to wash.
“Now is the time to shut down Moria for good,” Velges Vialojtis, a local municipal leader from Lesbos, told AFP news agency.
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The European Union has been divided over the years to deal with the mass arrival of migrants, mainly to Italy and Greece.
Italy and Greece have accused rich northern countries of failing to do more, while many central and eastern nations are openly resistant to the idea of taking in migrants’ quotas.
What is agreed?
According to the German report, other countries expected to have children include Switzerland, Belgium, Croatia, Slovenia, Luxembourg and Portugal.
The Interior Minister said the fire in Moria was “a sharp reminder for all of us to change in Europe”.
But a group of charitable and NGOs have written to the German government that more should be done, not for all minors, but for all migrants.
On Thursday, Greek Prime Minister Kiriakos Mitsotakis said that the migrant crisis was Europe’s problem, and that the EU needed concrete action to deal with it.
German Chancellor Angela Merkel spoke to Mr Mitsotakis over the phone and said she agreed that Germany would take some migrant children.
While visiting the burnt-out Moria site on Thursday, Mr Sinicas said it was “unbelievable” that the European Union had not yet had a unified migration policy.
He said the Commission’s proposal for a new agreement on migration and asylum, due to be introduced on 30 September, would “end this unacceptable situation”.
What caused the camp to catch fire?
According to local fire chief Constantino Theophilopoulos, more than three locations caught fire overnight on Tuesday. Further fires almost completely destroyed the camp.
The fire broke out hours after reports that 35 people had tested positive for Kovid-19 at the camp. Authorities placed the facility under quarantine last week when a Somali migrant was confirmed to have contracted coronovirus.
Eight of the 35 who tested positive for Kovid-19 are believed to have been found and isolated.
Greek migration minister Notices Mitrachi said the fire “started with quarantine seekers because of quarantine”. Some of those infected with the virus reportedly refused to go into isolation with their families.
However, he did not say that the arson was a deliberate action intended to destroy the camp.
But some migrants told BBC Persian that the camp was engulfed in flames after a scuffle between migrants and Greek forces.
What is being done for the migrants?
Greece has sent three ships to Lesbos to provide accommodation for some 2,000 migrants. The Blue Star Chios Ferry, which has a capacity of 1,000 people, has docked at the Lesbos port of Sigri. Two naval vessels have also been provided.
But authorities have also increased security on the island. Military personnel, riot police and water cannon have reached the spot.
On Thursday at a car park park outside a supermarket, hundreds of migrants, including families with young children, had to wait to distribute bottled water and food.
According to the news agency Reuters, “Natalie Malala, a newborn and eight-year-old girl, said,” There is no food for the baby, no milk for the baby. “
But there is strong resistance by local people to house them for a new camp. “We do not want another camp, and we will resist any construction work. We have faced this situation for five years, it is time for others to bear this burden,” said local leader Vangelis Violatzis Was quoted as saying.