AMSTERDAM (Reuters) - Australia and East Timor aim for an agreement over the disputed maritime boundary in resource-rich waters between their countries, a court said on Thursday, signaling a deal could be reached by next September.

Confidential meetings between the two countries have been "very productive" and would continue next year, the Permanent Court of Arbitration in The Hague said in a statement.

The court ordered compulsory arbitration in the case last month after East Timor requested the process against objections from Australia, which negotiated a revenue sharing agreement that gave it until 2056 to settle the boundary issue.

Australia played a critical role in East Timor's independence from Indonesia in 2002 and shortly after that negotiated the revenue sharing deal for the large Greater Sunrise oil and gas field. East Timor calls the deal unfair.

"All agreed we should aim to reach agreement within the timeframe of the conciliation process," the court said, referring to the compulsory arbitration. That process has a deadline of Sept. 19, 2017.

"I was very pleased to see a sincere willingness on both sides to come together in a spirit of cooperation," said Peter Taksoe-Jensen, who headed the arbitration talks.

"Both sides are to be commended for being willing to move beyond past differences and work hard to create conditions conducive to achieving an agreement."

East Timor appealed to the court for the arbitration that could determine the border through the Greater Sunrise oil and gas field. It has said that Australian espionage on its diplomats rendered recent agreements on it flawed.

East Timor says the boundary should fall halfway between it and Australia, which had argued that defining the border that way could prompt Indonesia to also seek to shift its sea border and gain ownership of disputed oil fields.

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 mean its development is on hold.

(Reporting By Anthony Deutsch; Editing by Tom Heneghan)