According to Reuters, locals seeking additional compensation threatened workers at the Hides gas conditioning plant site of the project.
Exxon Mobil's PNG subsidiary confirmed it had requested a group of people in the Hides area to cease the "illegal stop-work activities they are undertaking".
"Work has been temporarily suspended in the Hides area but is continuing throughout the rest of the project area," an Esso spokesperson said.
"The matter has been referred to the police."
Esso said steps were taken to engage with the group and it was disappointed with its recent actions.
"The community is also being impacted as people are unable to work due to threats made to our workforce," the spokesperson said.
"The group is aware that there is a formal grievance process with respect to land access, where adjudication can be made by a chief warden."
Esso is also stressing the need for the PNG LNG project to be completed on time, with first exports expected in 2014.
"Work stoppage actions are disruptive to the early work schedules, however, we continue to work with local leaders and the government to address concerns and avoid impacts on the project," the spokesperson said.