Authorities in Greenland have confirmed that four people are missing after a tsunami hit the area. "You have seen that in Greenland before", Jensen said.
In total, the settlement lived 101 inhabitants, 78 of whom were evacuated.
Police urged the citizens of Illorsuit, which also saw the large waves, to return to their homes, but warned of sirens that would signal people to seek higher ground in case of aftershocks.
Video taken in one of the villages and posted online shows a surge of dirty water coming ashore as frightened villagers panic. A helicopter and boats have been deployed to assist in the search-and-rescue effort.
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The Geological Survey of Denmark and Greenland said Sunday that an quake late Saturday with a magnitude of around 4.0 on the Richter scale struck northwestern Greenland near the village of Nuugaatsiaq.
Two people sustained serious injuries, and seven others less serious injuries, police said.
Police chief Bjørn Tegner Bay said he was unable to confirm whether there had been fatalities, according to KNR, Greenland's broadcasting corporation. It said surging water is reported to have destroyed 11 buildings there.
Meteorologist Trine Dahl Jensen told Danish news agency Ritzau that for such an natural disaster to hit Greenland was "not normal", as she warned of the risk of aftershocks.