One father, Yiannis Philippopoulos, told Greek television his nine-year-old twin girls were still missing.
He said he had seen his daughters, Sophia and Vasiliki, alive on TV news footage as they got off a fishing boat that had rescued them. But he has not since heard from them or their grandparents, who had been with them earlier that day.
There is no formal count of the missing. The fire brigade has received dozens of calls, but is unable to verify the exact number.
Relatives of those reported missing have posted photographs of more than 30 people online in the hope of tracing their whereabouts.
Coastal patrol boats combed the shoreline on Wednesday, searching for survivors and bodies, while rescue teams searched houses and cars.
The number of injured, meanwhile, continues to grow, and stands at more than 180, including two dozen or so children. Tourists were also caught up in the blaze, including one British man who was treated for burns.
Others have been evacuated to temporary accommodation.
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