Greek Holiday island is rising from the rubble brought by deadly quake.

Culture ministry employees assess the damage of a mosque at the Greek island of Kos.

Greek holiday island of Kos was struggling to recover from a quake that killed two people and injured hundreds, with tourists facing flight delays and the damaged main harbour closed for a second day.

The 6.7-magnitude tremor also left hundreds more injured in the Turkish resort of Bodrum, about 20 kilometres across the sea from Kos.

"Given the amount of people outside at the time, having only two victims is a miracle," deputy Kos mayor David Yerasklis told Kathimerini daily.

The undersea quake struck at 1:31 am Friday between Kos and Bodrum.

At the time, tourists in both places were out enjoying the nightlife.

On Kos, the upper facade of a two-storey nightclub collapsed on people outside, killing a 22-year-old Swede and a 39-year-old Turk.

Another 120 people were hurt, seven of them seriously, while some 360 people were injured in Bodrum many after jumping out of windows.

The badly injured on Kos were flown to hospitals in Athens and Crete, including two men from Sweden and Norway who are in critical condition.

The hospital on Crete on Saturday said the 23-year-old Norwegian who had lost his lower leg early on had to have his other leg amputated.

The 21-year-old Swede has serious head injuries and broken bones.

Police on Friday had given their nationalities in the inverse order.

Another 20 people remained hospitalised in Turkey, said Turkish Prime Minister Binali Yildirim, who sent his sympathies.

"Hardship, like joy, is shared where neighbours are concerned," Yildirim said.

Kos is one of Greece's top travel destinations, and particularly popular with British, German and Scandinavian tourists.

- No dramatisation -

The quake struck at the height of the tourism season, and Greek Prime Minister Alexis Tsipras on Friday warned against "dramatising" the issue.

"Creating a climate of exaggeration and dramatisation does not help restoring normality in daily life on the island," Tsipras' office said in a statement.

Government officials and expert divers on Saturday were inspecting Kos's harbour, which was cracked by the tremor and has been declared unsafe for use.

But the rest of island's infrastructure network including roads is mostly intact, they stressed.

Ferries have been rerouted to the smaller port town of Kefalos in west Kos until repairs are made.

"All scheduled ferry services are now running from Kefalos, both incoming and outgoing," a Kos coastguard operator said.

Many people spent the night outdoors as a precaution, setting up tents in parks and squares, but officials noted that the majority of hotels were unaffected by the quake.

Deborah Kinnear, a 35-year-old psychologist from Glasgow, said her family initially thought of returning home but no flights were available.

"I think calm is being restored," she said after spending the night outdoors.

"Last night wasn't too bad. Hoping the worst is over... this has been one of our best holidays," she said.

At Kos airport, delays continued for a second straight day with over 50 outgoing flights scheduled. Over 20 flights had landed by midday Saturday.

"There is no problem at the hotels, the tourists have dealt calmly with developments," Constantina Svynou, head of the local hotelier association, told Ta Nea daily.

- Monuments closed -

Some areas of the port town were still without water, however.

The UN refugee agency said no injuries were reported among the 800 migrants and refugees housed on the island, which is one of the main gateways into Europe for people fleeing war and poverty.

But asylum procedures have been curtailed until at least Monday as the quake damaged passport inspection facilities at the harbour.

Many archaeological and medieval monuments including the medieval Knights of St John fortifications near where the deaths occurred have also been closed until further notice.

The quake toppled the minaret of a historic 18th century mosque, damaged a church and knocked boulders off the fortifications.

In Bodrum, three buildings collapsed and another 32 were damaged, the Turkish PM said.

Turkey and Greece sit on significant fault lines and have regularly been hit by earthquakes in recent years.

On Saturday, researchers at Thessaloniki's Aristotelio University said Friday's tremor had been caused by a fault line that sparked a 1493 quake estimated to have killed some 5,000 people.

This year alone, Turkey's western Aegean coast was hit by several significant tremors.

In June, a 6.3-magnitude earthquake gutted a village on the Greek island of Lesbos, killing a woman and leaving more than 15 injured.