The plant's second train is also operational, with the company expecting to reach full capacity in May.
Exports from the LNG plant outside Port Moresby have also resumed.
ExxonMobil PNG managing director Andrew Barry acknowledged there was still plenty of relief work to do after the magnitude 7.5 earthquake that struck Hela province in late February.
"I am extremely proud of the spirit of partnership and commitment that has been displayed by so many in recent weeks to help our business and communities through these events," Barry said.
"We know there is a lot of work to be done and communities are still struggling.
"It will take some time to restore homes, food gardens, health centres and education services, and we remain committed to working with the government, our community partners and aid organisation to continue providing assistance and support in the weeks and months ahead."
To date the company has provided nearly 3.5 million Kina towards humanitarian relief.