No people live in the immediate area but it’s situated in a national park popular with tourists.
An area to the north has been evacuated.
Hundreds of earthquakes have been detected every day, the strongest at 4.7 magnitude just before midnight on Thursday – although on Friday afternoon the volcano was calmer.
“If an eruption happens, we need to assume that it will happen quickly with magma migrating towards the surface. It could also enter a state of equilibrium and nothing happen,” said Kristin Jonsdottir, Scientific Coordinator at the Icelandic Earthquake Monitoring Office.
It’s thought an eruption would cause ice from a glacier to melt, bringing massive flooding from a glacial river across a wide area.
Measures have been taken to ensure emergency power supplies.
There are also fears that air travel could be as badly disrupted as it was in 2010 when the Eyjafjallajökull volcano erupted, sending an ash cloud towards Europe.