A group of Hides landowners started up a "stop work" campaign at PNG LNG project sites in the area about two weeks ago - and disruptions included threats made to project workers.
A "source" recently told The National the project "evacuated" workers on Sunday and also predicted "it would be the end of the project if the closure continued this week".
But the Exxon spokesperson's views were not as dramatic.
"The project has not evacuated workers from the Hides area," she said.
"Work in the Hides area has been stopped for some time now by this unlawful activity, and some workers have been demobilised from the area because they are unable to work."
She confirmed work remained temporarily suspended due to the action of some members of the local community.
There are no signs a sudden end to the project is on the cards either.
"While work stoppage actions are disruptive, we remain on track for first gas in 2014," the spokesperson added.
She said Exxon's PNG subsidiary Esso Highlands and the national government are engaged with community leaders to understand and attempt to resolve issues so Hides area construction work can resume.
"The project encourages continued dialogue between communities, the government and the project to address issues as they arise, without impact to ongoing project activities.
"Esso Highlands Limited, with the government, has taken steps to engage with the group in question to understand their issues. It is disappointing that the group continues to halt work on the project."
Key cabinet ministers were expected to discuss a range of measures to address the situation yesterday, including the possible declaration of a state of emergency in the province along with bringing in troops and additional police.
But the National newspaper reported this morning that the planned meeting did not go ahead "due to a lack of quorum" - meaning some ministers probably did not show up.
Hides 4 Landowner Umbrella Association chairman Chris Payabe told the PNG newspaper the possible move to declare a state of emergency was intimidating and uncalled for.
He reportedly represents 12,000 people in the Hides 4 Petroleum Development Licence and his group was seeking 99 million kina ($A44.2 million) of compensation from ExxonMobil for various project activities in the area.
The aggrieved landowner group has also sought upgrades to the Hides-Komo road - which was cut off by a devastating landslide earlier this year - and to a local health centre and community school building.
One of the key PNG LNG project activities in the area is the construction of the Hides Gas Conditioning Plant.