Around 300 refugees and migrants had by Sunday evening moved into a new camp facility being built by the Greek army in a former military shooting range in Kara Tepe, on the island of Lesbos.
Soldiers have set up between 300 and 350 tents and continued working into the night.
But many of the refugees and migrants are reluctant to move into a new camp that will be manned by police. They fear it will be a prison.
Meanwhile, almost 10,000 prepared to sleep rough another night in the stretch of the road between Kara Tepe and the outskirts of Mytilene, the capital of Lesbos.
Greece’s prime minister demanded on Sunday that the European Union take a greater responsibility for managing migration into the bloc, as Greek authorities promised that 12,000 migrants and asylum-seekers left homeless after fire gutted an overcrowded camp would be moved shortly to a new tent city.
Kyriakos Mitsotakis blamed some residents at the Moria camp on Lesbos for trying to blackmail his government by deliberately setting the fires that destroyed the camp last week. But he said this could be an opportunity to improve how the EU handles a key challenge.
“It (the burning of Moria) was a tragedy. These images were bad. It was a warning bell to all to become sensitized. Europe cannot afford a second failure on the migration issue,” Mitsotakis said Sunday at a press conference in the northern city of Thessaloniki.
Human rights activists have long deplored the squalor at the Moria refugee camp, which was built to house 2,750 but was filled with some 12,500 people who fled across the sea from Turkey.
Since the fires, which came after the camp faced a coronavirus lockdown, thousands of people have camped out in the open on highway near Moria under police guard. Many have protested the Greek government for refusing to allow the homeless migrants to leave Lesbos for the Greek mainland. Greek residents are also unhappy that their island is being used as a dumping ground for migrants.
Mitsotakis said he has been in touch with French President Emmanuel Macron and German Chancellor Angela Merkel over the reallocation of at least some migrants from Moria, but he said there will be a new, permanent refugee camp on Lesbos.
The Greek army has been setting up tents at a former artillery range, about 4 kilometers (2.5 miles) from the old camp.
Migration Minister Notis Mitarakis said an estimated 1,000 Moria residents would be relocated to the army-built tent city late Sunday and that getting everyone housed at the new site would take several days.
"At the moment, it’s happening on a voluntary basis,” Mitarakis told Greek TV station Open TV.
Mitarakis said those entering the new camp would undergo rapid testing for coronavirus and that five new cases have been found so far.
At the Vatican, Pope Francis expressed solidarity Sunday with the migrants on Lesbos and called for “dignified” welcome for them. Francis had visited the Moria camp in 2016, bringing back to Rome with him 12 Syrian refugees.