|Map: BBC News|
Mr Gusmao, a former president of East Timor, said his country would appeal to Australians' sense of fair play to push their government into meaningful talks.
"If we go to the media and if we raise awareness, it is not because we want people to be against Australia but just to say 'oh yes, it is unfair'," Mr Gusmao said.
Mr Gusmao said he hopes to win sympathy from Australian activists, who had championed East Timor's struggle for independence from Indonesia.
He also wants support from Australian soldiers who served as peacekeepers in the impoverished nation.
East Timor has sought for years to renegotiate a treaty governing oil and gas revenue sharing arrangements that was signed with Australia soon after it gained statehood in 2002.
"From the beginning we asked Canberra to talk," Mr Gusmao said.
"They wouldn't want to blow up all of these issues. We are neighbours, we have problems, we sit down, we talk — but nothing."
East Timor argues the sea border, undefined since it was a Portuguese colony, should fall halfway between it and Australia — which it says would put several oil and gas fields in its territory.
Under the treaty, East Timor shares revenues from these fields — from a mooted half share of the as-yet undeveloped Greater Sunrise fields to 90 per cent of the currently producing Bayu-Undan and Kitan fields.
Allegations that Australian spied on Timorese negotiators fuelled controversy over the treaty.
The issue was taken to the International Court of Justice before East Timor officially dropped the case in June.
However, East Timor is still pursuing international arbitration over both the maritime border dispute and a tax case involving a pipeline from the existing fields to Australia.
Australia warns that defining the border the way East Timor wants may prompt Indonesia to also seek to shift its sea border, and thus gain ownership of disputed oil fields.
An Australian government map shows most of the Greater Sunrise fields in its waters, but with a warning they could be claimed by Indonesia if the border moves.
East Timor's map shows the fields within its claimed share of the Timor Sea.
Greater Sunrise is 33 per cent owned by Woodside, the operator. Its co-owners are ConocoPhilips, Royal Dutch Shell and Japan's Osaka Gas Co Ltd.
Greater Sunrise contains an estimated 5.1 trillion cubic feet of gas and 226 million barrels of condensate, although the border dispute, and low gas prices, means development is on hold.