The eruption is said to have started north of Grindavik at eight o'clock on Sunday morning, local time. The eruption was preceded by a series of earthquakes at the crater Sundhnúksgíga during the night.
The magma is now reported to be floating under the Svartsengi power plant and out to sea. This is said to be "much closer" to Grindavik than at the time of the eruption on December 18.
"It's hard to say how big the eruption will be," Benedikt Ófeigsson, an expert on natural disasters at the Icelandic Meteorological Institute, told state broadcaster RÚV.
Residents have been evacuated
Residents of Grindavik are said to have been evacuated at four o'clock during the night to Sunday, RÚV writes. Traffic to the city is closed. Now Iceland is gearing up for another relief effort, including with the help of an aid center in the capital Reykjavik.
Grindavik is largely without power.