Greece's coast guard has launched a search and rescue operation off the eastern Aegean island of Chios for two men reported missing after a migrant boat made it to shore from nearby Turkey.

The coast guard said a total of 36 people had been found safe early Thursday. Survivors reported the two men missing.

Of those rescued, eight had made it to shore, 23 were found on a rocky part of the coast and a further five were found in the dinghy they arrived in.

Coast guard and European border agency Frontex vessels and an air force helicopter were conducting the search.

Hundreds of migrants continue to arrive on Greek islands from Turkey each week, although the numbers are far reduced from the height of the influx in 2015.