Wong travelled to Papua New Guinea before visiting Timor-Leste this week to pressure Australia's impoverished neighbour into an agreement with Woodside Energy Group
The trip came shortly after the Timor-Leste petroleum minister Victor da Conceicao indicated the country would consider partnering with China to fast-track Greater Sunrise development if the Australian government did not "intervene" in negotiations with operator Woodside.
He made the comments via an interview with the Australian Financial Review.
The long-stalled LNG project is of significant importance to Timor-Leste as it would ensure the state's sovereign wealth fund does not run out.
"I have said this has been stuck for many years, I've said to the president and to others we need to unstick it," Wong told journalists at a joint press conference alongside Timor-Leste foreign minister Adaljiza Magno.
"That will be best done respectfully and directly, not through the media."
Wong called for respect in negotiations between Timor-Leste and Woodside.
The Greater Sunrise fields sit 450 kilometres north-west of Australia and 150km offshore Timor-Leste across both country's maritime borders.
Woodside wants to send gas from Greater Sunrise to Darwin for processing and export.
Timor-Leste wants a greenfield plant in its south coast.
Both parties are at a stalemate.
"It is important to recognise the joint venture partners need to come to an agreement for the project to proceed," Wong said.