Thousands of people have been evacuated from Iceland's coastal town of Grindavik after a series of strong earthquakes in the southwest of the country risked a volcanic eruption.

"The evacuation of Grindavik ended around one o'clock in the morning without any problems," Iceland's Department of Civil Protection and Emergency Management said on Saturday.

The evacuation decision was taken on late Friday after the country declared an emergency phase, citing a “magma tunnel that is forming could reach Grindavík.”

"The latest data from the Met Office show considerable displacement and a large magma tunnel that is forming and may open, which would then run from south-west to north-east," the department said in a statement on Friday.

"We want to reiterate that residents MUST evacuate their homes and leave the town," it said. "But we also want to reiterate that this is not an emergency evacuation, there is plenty of time to prepare, secure things and drive out of town calmly."

The department stressed that the country is "dealing with events that we Icelanders have not experienced before, at least not since the eruption in Vestmannaeyjar."

Nearly 800 quakes were recorded between midnight and 2:00 p.m. on Friday, according to the Icelandic Meteorological Office.

Iceland is home to a total of 32 active volcanos.