The report said on Wednesday that defensive walls were built around the masts, and there was hope that the walls would hold lava. The Icelandic Foreign Ministry is closely monitoring the situation, the report said.
Grindavik Mayor Fannar Jonasson has expressed concerns that defenses might break.
"It has to be expected that if it continues like this, then something might start to give way," he said on air on RUV.
The eruption in the area of the volcanic hill Sundhnukur on the Reykjanes Peninsula began on Wednesday afternoon. Before the eruption, authorities ordered that people be evacuated from Grindavik and the Blue Lagoon geothermal spa.
The lava is flowing toward Grindavik, which is located to the south of the eruption cluster. The city has no power supply, and all but one of the roads leading into the city are covered with lava. Three citizens who refused to evacuate reportedly remain in the city.
Following the eruption, police declared a state of emergency in the country.
January's volcanic eruption destroyed several houses in Grindavik, which has a population of about three thousand people.