Wednesday's fire, which followed a blaze set the day before, turned the sprawling site into a mass of smouldering metal and melted tents.
Thousands assembled for a protest demanding to be allowed to leave the island.
Moria had been under a lockdown until mid-September after the first virus case was identified in a Somali man who had been granted asylum and left for Athens but later returned to the camp.
"It is a tragic opportunity for migrants to leave. Moria is a monstrosity", Dimitris Koursoubas, a senior official responsible for migration in the northern Aegean islands, told Reuters. Critics say the camp is a symbol of failures in the EU's migration and refugee policy.
The local mayor has rejected efforts to build new temporary camps as "unrealistic" and residents have tried to stop the construction of new camps by setting up roadblocks.
Authorities have now set up a new 3,000-capacity camp at Kara Tepe, a few kilometres (miles) from the destroyed camp, regularly criticised by the United Nations and rights groups for overcrowding and dismal sanitary conditions.
"We are sleeping in the dirt or on the road under the open sky", a group of migrants from the former camp said on Facebook, noting that some people had even found shelter under the trees of the local Greek cemetery.
But with other European nations accepting only a small trickle of refugees, thousands remain trapped in the Greek camps in usually dismal health conditions.
"Moria finished", said Zohra, a 25-year-old Afghan woman.
Francis later revealed that in its own concrete response, the Vatican had negotiated in the days leading up to the Lesbos trip for the papal plane to carry back with him three Syrian families.
Homelesss migrants and refugees rest as they spend the night at a gas station near Mytilene
Migration Ministry officials said on Saturday that the plan was to eventually provide tents for all the homeless and accelerate the asylum procedure, with minister Notis Mitarachi saying it would take "five days" to get everyone inside. Cities and regional governments in Germany have also offered to take in people, but this can only happen if the federal government in Berlin allows them.
The government has agreed in principle to accept around 20 unaccompanied minors from the Moria asylum camp in Greece that has been devastated by fires.
Image; Migrants wait in a queue for food distribution near Mytilene town, on the northeastern island of Lesbos, Greece, Saturday, Sept. 12, 2020.
German Interior Minister Horst Seehofer said Friday that 10 European Union countries had agreed to participate in taking in the unaccompanied children and that talks were ongoing with others.
European Commission vice-president Margaritis Schinas, who visited Lesbos on Thursday, said they had organised the transfer of 400 unaccompanied minors to the mainland with a view to their relocation in Europe. He said Germany and France would take the largest share, "about two-thirds" of the 406 children who had been living at the camp without parents or guardians.
Greek authorities began admitting migrants to temporary tent accommodation outside the main port of Mytilene.
The clashes broke out near a temporary camp built by Greek authorities.
Some of these demonstrators wore masks at the tightly packed bunch of folks who lately had lived at the camp, which had heaps of supported coronavirus instances before it burnt down on Tuesday and Wednesday night.
The Greek authorities claim the fires were deliberately lit by asylum seekers who were angry with quarantine measures that had been introduced after 35 migrants tested positive for Covid-19.
Android 11 Go Edition Arrives With Gesture Navigation
Google says this is going to be a bump from the previous version which was made to support devices with less than 1.5GB of RAM. After an extended period of time, those will be auto-reset so that you don't accidentally allow video access, for example.