Australia has rejected the jurisdiction of an international tribunal on which East Timor is relying to deliver a greater slice of oil and gas revenue.
East Timor remains incensed by claims Australia spied during negotiations for a Howard-era treaty to share oil and gas deposits in the Timor Sea.
The tiny nation has invoked a never-before used "conciliation commission" under the international law of the sea in a bid to end a bitter impasse over drawing a maritime boundary.
Former prime minister and independence hero Xanana Gusmao told the opening hearing of the commission on Monday that East Timor was not asking for favours or special treatment, just its rights under international law.
"So many East Timorese people have fought and died for our sovereignty," Mr Gusmao said.
He said he was "shocked and appalled" when told Australia had bugged the tiny nation's cabinet office in 2004. Australia has prevented a former intelligence agent known as "Witness K" from appearing at a separate case brought by East Timor.
But at a hearing at the Permanent Court of Arbitration at The Hague, Australian officials denied the spying allegations and said East Timor should respect existing treaties to divide undersea resources.
"We're here today because Timor Leste wants a different deal," Foreign Affairs deputy secretary Gary Quinlin told the hearing.
Australia argued the commission had no jurisdiction to conduct hearings on maritime boundaries, and said the existing treaties are in full compliance with international law.
The conciliation was invoked in April after Prime Minister Malcolm Turnbull knocked back a plea from his East Timorese counterpart, Rui Maria de Araujo, asking for fresh negotiations.
International law specialist Don Rothwell said the conciliation process was "completely new territory".
Participation is compulsory, but the outcome is not-binding - a point Australia has been quick to emphasise.
But Professor Rothwell said the commission was not merely a legal process, but an attempt to find an acceptable solution for both sides.
Australia has committed to participate in the conciliation, even if it loses the challenge to jurisdiction. The conciliation commission is made up of five international legal experts.
The existing treaties, signed soon after East Timor achieved independence, divide undersea resources and Australia said the deal had "benefited both our countries", with East Timor since accumulating a fund worth more than $16 billion.
But East Timor's lawyers told the hearing a 2006 treaty - known as "Certain Maritime Arrangements in the Timor Sea", or CMATS - had failed and outlived its usefulness.
The CMATS treaty created a 50-50 split of the rich "Greater Sunrise" field, and put off negotiations on a final maritime boundary for 50 years.
East Timor now argues the resources should be under its control - while Australia claims the field sits mostly within its territory.
La Trobe University's Bec Strating, who has written extensively on the dispute, said the conciliation appeared an effort by East Timor to create public pressure.
"Timor Leste has increasingly viewed permanent maritime boundaries as a core aspect of sovereignty and independence," Dr Strating said.
But she said a public relations campaign in Australia was unlikely to sway the Turnbull government's approach.
"If the Australian public can't get them to change policy on Nauru and offshore detention, what hope do they have on Timor Leste," she said.
Labor pledged at the last election it would enter into "good faith" negotiations on the maritime boundary and shadow foreign affairs spokeswoman Penny Wong said on Monday: "We need this dispute settled in fair and permanent terms."
Dr Strating said the conciliation process did not address the central problem of a power imbalance between the countries.
"Australia has the upper hand in this. Australia doesn't urgently need oil and gas revenues. Timor Leste does," Dr Strating said.
East Timor's petroleum fund shrank for the first time last year, the balance falling by $321 million after a drop in global oil prices and an increase in government spending.
Swinburne University Timor specialist Mike Leach warned if the jurisdictional challenge went against East Timor, the tiny nation could move to terminate the CMATS treaty.
