Videos of people searching through various buildings' debris went viral on social media as well. CNN Turk showed one woman being pulled out alive. The city's mayor said almost 20 buildings had collapsed.
Reports said the quake caused mini-tsunami on the Aegean island of Samo as several buildings were damaged.
But scenes of devastation suggested the toll could rise.
Mitsotakis called Erdogan to offer condolences after several deaths reported in Izmir.
Aerial footage on Turkey's NTV television showed entire city blocks turned to rubble.
Rescue officials and youth joined hands to search for survivors in the rubble.
Israel's once-close relations with Turkey have deteriorated in recent years amid tensions with Islamist President Recep Tayyip Erdogan.
Reports are still coming in, but the magnitude 7.0 quake took place at 13:57 local time a few kilometers due North of Agios Konstantinos, on the north coast of the island in the eastern part of the Icarian Sea.
People stand outside their homes after a strong earthquake hit the Turkish city of Izmir
On Samos, Greece, where a tsunami warning was issued, two teenagers died after being struck by a wall that collapsed.
"We have never experienced anything like it", said George Dionysiou, the local vice-mayor.
Water rose above the dock in the main harbour of Samos and flooded the street, and residents were also told to stay away from buildings as aftershocks rattled the area.
Turkey is on the 14-day quarantine list for British tourists, while Greece and most of its islands including Samos are on the approved list for travellers from England, with Scotland and Wales applying their own rules.
Cooperation between the two countries after the devastating 1999 quake led to a period of warmer ties between them. Earlier, their foreign ministers spoke and said they were ready to help one another, Ankara said.
"Closely following the developments of the strong quake that hit the Aegean Sea off Greece and Turkey".
Earthquakes are a common occurence in Turkey; almost 17,000 people died in a quake in the western city of Izmit in 1999.
People walk past a destroyed house after an quake in the island of Samos on October 30, 2020.
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