Greece has resettled hundreds of migrants in a temporary new tent facility after a fire destroyed their overcrowded refugee camp on the island of Lesbos and hopes to have moved all of them this week, government officials said on Monday.

More than 12,000 people, mostly refugees from Afghanistan, Africa and Syria, are without shelter and have to sleep out in the open without proper sanitation after a fire tore through the Moria migrant camp last Wednesday.

Greece is now registering the migrants and testing them for COVID-19 before channeling them into the temporary tent camp, government spokesman Stelios Petsas said, though a police officer said some were refusing to move to the facility.

"We expect that in the next three to four days all will be housed, a bit less than the (total number of) roughly 12,000 homeless," he told reporters.

The authorities have already moved some 400 minors from the island to the Greek mainland since the blaze for possible resettlement in other European countries.

About 600 migrants have so far been resettled in the temporary tent camp, and 14 of them have tested positive for COVID-19, a government official said.

In the chaos following last week's fire, authorities lost sight of 35 people who had tested positive, deepening fears of an outbreak among migrants sleeping closely together without proper sanitation.

Petsas repeated on Monday the government's suspicion that the fire was started deliberately "by migrants who wanted to blackmail the government to leave the island." An investigation into the cause of the blaze is underway.

Prime Minister Kyriakos Mitsotakis said on Sunday that Greece would build a permanent new migrant reception center to replace the Moria facility.

Germany's Bild newspaper reported on Monday that Berlin is considering taking in thousands of refugees from Lesbos as a one-off gesture and also wants the Moria camp to be rebuilt and run by the European Union.