In a case filed in Washington, the International Labor Rights Fund (ILRF) says Exxon was implicated by virtue of the local army units it hired to protect its natural gas fields in Aceh province, northern Sumatra.
It alleges that Exxon provided the Indonesian military with equipment to dig mass graves, as well as building interrogation and torture centres. Exxon denies all the allegations.
The action is being taken under the Alien Tort Claims Act, which allows US jurisdiction over acts committed outside the US.
Hard evidence
Terry Collingsworth, a lawyer for the ILRF, said Exxon knew from the beginning about the security forces' reputation of brutality towards ethnic minorities.
"This is the first time we actually have evidence that the oil company has supported the instrumentality for the human rights violations," he said.
An Exxon statement said the company was "deeply troubled" by the violence in North Aceh and was concerned for the safety of its staff and subcontractors.
"Our company rejects and categorically denies any suggestion or implication that it or its affiliate companies were in any way involved with alleged human rights abuses by security forces in Aceh," it added.
Operations suspended
Thousands of people have died in the long-running separatist campaign by Aceh militants against the Indonesian Government - more than 700 have died this year alone.
Despite pressure from the Indonesian government, which is losing an estimated $100m a month in liquid natural gas (LNG) revenues, the company has so far refused to restart its operation, although it is considering resuming its operation.
Exxon sites have been the scenes of fighting and staff have been threatened and even kidnapped. Vehicles have also been burned and shots have been fired at Exxon chartered aircraft.
Exxon abroad
The Asia-Pacific region contributes about 13% of ExxonMobil's worldwide production of oil and gas.
In Indonesia, the company produces gas from the country's largest natural gas field - Arun - which is then processed by the state owned oil and gas firm Pertamina.
Last year, this gas yielded 118 cargoes of the valuable LNG which was shipped to customers in Japan and Korea.
Other exploration, appraisal and development planning activities are currently under way in the region.
Many of the world's potential hotspots for oil are also located in areas of political unrest such as Nigeria and Algeria.
Oil companies are often forced to weigh the risks of entering a particular area against the value of the assets they believe to be awaiting discovery below the surface.