The north Atlantic island, where almost 320,000 people live, is a hotspot of volcanic and seismic activity as it straddles a fault in the earth's surface.
The Civil Protection Department said in a statement that recent small quakes in an area under the sea about 20 km (12 miles) off the north of Iceland had prompted it to issue a warning to local people.
It said such shocks, one of which was a magnitude 5.6, often led to stronger quakes. Warnings were issued when there were grounds to expect a natural or manmade event that could threaten health and human safety, it added.
"People are anxious because they don't know what might happen," said Amundi Gunnarsson, chief of the fire brigade in Fjallabyggd, one of the small towns in the area, and a member of the Civil Protection Department.
"At the same time, life goes on as usual. People are going to work and children are going to school, but everyone is on alert," he told Reuters by telephone.
The coastal area in the north is home to several small towns and a population of several thousand people.
The biggest town in the north of Iceland, Akureyri, has a population of about 17,000 people, and lies roughly 100 km south of the seismic activity.
Geologist Benedikt Ofeigsson said houses in Iceland could typically withstand quakes of a magnitude about 7.
"Of course there could be some damage to in walls and concrete in such strong earthquakes, but what is important that houses have stood firm," he told Reuters.
(Reporting by Robert Robertsson, writing by Patrick Lannin; Editing by Alistair Scrutton and Keith Weir)
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