Greek officials said many of the 13,000 migrants who lived in the camp would be temporarily placed on ships at a nearby port or in tents flown in from Athens.
About 400 teenagers and children have been transferred to the mainland.
At a debate in Parliament on Thursday, Nicolaus Fest, of the Identity and Democracy group, questioned why the incident was being debated “so soon.”
The tragedy was added at short notice to the agenda of the Committee of Civil Liberties, Justice and Home Affairs.
But Fest, who said he wanted to raise a “point of order” on the issue, told the Committee there were media reports that the fire had been started by the refugees themselves.
He told MEPs, “Why are we putting ourselves at the mercy of events like this by putting on the Parliament's agenda anything that is to do with refugees?
“This was a tragic incident which fully deserves our attention now and we need to discuss what happened on Lesbos today” Tineke Strik MEP
“This cannot be allowed to happen because we don’t have time to deal with it all. This ad hoc approach is wrong.”
The German deputy added, “We should wait for the criminal investigation into this incident to be concluded. It is too early to start a debate now.”
But his comments were condemned by another Committee member, Dutch Greens MEP Tineke Strik.
She told the meeting, “I firmly reject these allegations. This was a tragic incident which fully deserves our attention now and we need to discuss what happened on Lesbos today.”
The EU has offered to help with the response to the fire, with European Commission President Ursula von der Leyen saying the main priority was “the safety of those left without shelter.”
German foreign minister Heiko Maas described the fire as a “humanitarian disaster” and tweeted about “the distribution of refugees among those willing to accept admission in the EU.”
“Why are we putting ourselves at the mercy of events like this by putting on the Parliament's agenda anything that is to do with refugees? This cannot be allowed to happen because we don’t have time to deal with it all. This ad hoc approach is wrong” Nicolaus Fest MEP
The refugee camp fire has as again put asylum and migration back on the agenda and coincides with a new proposal, expected this month, from the Commission on how to distribute people who arrive at Europe’s southern borders.
On Wednesday, Commission Vice-President Margaritas Schinas said Europe “can’t fail again, can’t fail twice” on such an important matter.
Council President Charles Michel is due to travel to Greece, Cyprus and Turkey later next week where he will discuss the migration issue.
Meanwhile, the Socialists and Democrats group in Parliament says it “strongly reiterates” its call for the “immediate evacuation of the overcrowded Greek island camps.”
This comes after the first COVID-19 case reported by Greek authorities in the Vial refugee camp on the island of Chios, which with 3,800 people is three times over capacity.
Dutch member Kati Piri, S&D deputy leader responsible for a strong and values-based Europe in the world, said, “The first known Coronavirus case inside one of the island camps is beyond alarming. Due to the constant overcrowding of the camps, calls for measures like isolation or social distancing are simply delusional.”
“Due to the shortage of soap and water people are not even able to follow basic hygiene like washing their hands to contain the virus. As the health situation of many people has already deteriorated due to the poor conditions in the camps, the risk of the virus causing severe symptoms or even leading to death is very real.”
Further comment comes from Birgit Sippel, S&D spokesperson on Civil Liberties, Justice and Home Affairs, who said, “It is a humanitarian scandal that Member States do not make good on their promise to take in refugees from the Greek island camps.”
“Since March, ten EU countries have agreed to accept at least 1,600 refugee children from overcrowded camps on the Greek islands – but only a fraction of this number have actually been relocated.”
The German MEP added, “My own home country Germany committed to receiving 928 refugees until the end of August, but has until now also failed to fulfil its promises.”
“This is unacceptable – even more so if you look at the different federal states within Germany and individual cities willing to take in even more refugees. We will be on Member States’ heels to make sure they live up to their promise.”