More than 12,000 people, mostly refugees from Afghanistan, Africa and Syria, were left without shelter, proper sanitation or access to food and water after a fire tore through the overcrowded Moria migrant camp last Wednesday.
At a temporary camp in the Kara Tepe area with 5,000 beds available, only about 1,000 people had moved in so far, according to a government official, adding that more space was being made available.
Migrants wearing masks as a precaution against the coronavirus queued outside the camp gates to receive water, food and blankets from aid workers before they entered.
COVID-19 tests were also carried out, and at least 25 people tested positive, further complicating attempts to resettle asylum seekers.
But many thousands more were reluctant to enter the tent camp, a police official said, fearing that life there would be no better than the squalid conditions they endured in Moria and hoping to be allowed to leave the island.
Thousands of people, including women and children, spent the night in makeshift tents on a road outside the temporary camp.
"We have informed them that they must come into the facility, but they have refused," the police official said, speaking on condition of anonymity. "They want to leave the island."
Germany could take in up to 1,500 people stranded by the Moria fire, government sources said on Tuesday, in addition to 100-150 Berlin has already agreed to take in.
Only a few hundred migrants, mainly unaccompanied minors, have been moved off Lesbos. Greek officials have said there will be no mass transfers and all asylum seekers will have to go into the new shelter.
"No one will leave Lesbos without having first entered the temporary camp," Citizen Protection Minister Michalis Chrisohoidis told Skai radio.
Prime Minister Kyriakos Mitsotakis said on Saturday that no matter what, a permanent migrant reception center would be set up on Lesbos to replace the overcrowded refugee camp destroyed last week's blaze.European Council President Charles Michel, who arrived in Athens on Tuesday, was expected to visit Lesbos in the evening.