The police operation, which included 70 female officers, was being assisted by officials from the National Public Health Association who were testing the migrants for coronavirus.
A police source said no force would be used, and officials were trying to convince the migrants to move voluntarily. So far 450 people had been transferred in the morning operation.
Until now some 1,200 migrants had entered a new tent camp set up by authorities to house migrants left homeless from the Moria camp fire.
But one week later, many had still refused to enter the camp and have been sleeping on the streets, in parking lots, and in forests.