The aviation colour code over the area has been changed from green to yellow as a precaution, the met office said, but the volcano's remote location in the heart of southern Iceland's uninhabited highlands means no infrastructure is at risk.
The series of seismic events lasted for about three hours before subsiding slightly, the met office said in a statement.
"Earthquakes continue to be detected in the area and it is too early to say whether the swarm will fade away," it said.
The largest earthquake registered a 5.1 magnitude, it said.
The met office said the earthquakes were "consistent with increased inflation due to magma accumulation" under Bardarbunga.
"The activity will be closely monitored but it is difficult to say what the development will be at this point," the met office said.
The caldera or hollow of the central Bardarbunga volcano is about 65 square kilometres (25 square miles) and ice-filled.
It is one of six volcanic systems located under Europe's biggest glacier Vatnajokull.
In the event of a subglacial eruption, there is a risk of an ash eruption and subglacial flooding from under Vatnajokull.
If an eruption were to occur outside the glacier, it would be a lava eruption, the met office explained.
"Seismic activity has increased in Bardarbunga in recent months," it said, with Tuesday's earthquake swarm the largest since Bardarbunga's last eruption in 2014-2015 which lasted six months.
That eruption created Iceland's biggest basalt lava flow in more than 230 years but caused no injuries or damage.
Iceland has seen seven volcanic eruptions in a year near the southwestern fishing village of Grindavik, leading to the evacuation of the town.
Iceland is home to 33 active volcanic systems, more than any other European country.
It is located on the Mid-Atlantic Ridge, a fault in the ocean floor that separates the Eurasian and North American tectonic plates and causes earthquakes and eruptions.
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