Two asylum seekers recently arrived on Greece's Lesbos island, the site of the country's biggest migrant camp, have tested positive for the coronavirus, migration ministry sources said on Friday.

The cases, doubling the island's COVID-19 infection tally on to four, were among 70 arrivals there so far during May.

Since March 1, all migrants who reach Lesbos have been quarantined away from the island's camps. Those include the overcrowded Moria facility, hosting more than 17,500 asylum seekers by the latest official count on May 13 and frequently criticised by aid groups for poor living conditions.

There have been no documented coronavirus cases there, however.

Greece has so far largely kept its its COVID-19 outbreak contained, with 2,770 cases and 156 deaths reported by Thursday evening. Authorities have since May 4 been gradually easing the lockdown they imposed in mid-March.

Lesbos lies just off the Turkish coast, and hundreds of thousands of migrants and refugees have used the island as a staging post in recent years in their attempt to get to mainland Europe.

In March 2016 an EU-brokered accord with Turkey all but halted the migrant flow, but meant the numbers of persons stuck on Greece's outlying islands built up while their claims for asylum were processed.