"We have to do our duty by demanding claims to the company responsible for the oil spill," Yudhoyono said in his opening speech Thursday at a Cabinet plenary session.
Thai-owned PTTEP Australasia operated the Montara exploration well in 250 feet of water between East Timor and Australia. It began leaking Aug. 21, 2009, and continued for 10 weeks, eventually causing the drilling rig West Atlas to catch fire.
PTTEP made several attempts to "kill" the well but the leak wasn't stopped until Nov. 3.
PTTEP estimated that 300-400 barrels of oil a day was pouring into the ocean but the Australian Department of Resources, Energy and Tourism said in October it could have been as much as 2,000 barrels a day.
Non-profit group the West Timor Care Foundation estimates that 75 percent of the 35,000-square-mile area of oil-affected waters from the spill is located in Indonesian fishing territory.
While Yudhoyono didn't say how much compensation he was seeking for the fisherman, some estimates in Indonesia are around $30 million, the Australian Broadcasting Corporation reports.
In the Indonesian province of East Nusa Tenggara, some 7,000 fishermen and more than 10,000 coastal communities rely on the Timor Sea and seaweed cultivation as a means of support.
The oil spill caused thousands of fishermen and seaweed farmers in Indonesia to lose their source of living, making it "a humanitarian tragedy of huge proportions," a representative for the Timor Sea Traditional Fishermen's Alliance told The Jakarta Globe last month.
He said thousands of people were considering migrating to Sumatra to find a new way to make a living.
Prior to the oil spill, seaweed farmers in the Rote Ndao area, for example, produced at least 7,334 tons of seaweed annually. Following the spill, production dropped to 1,512 tons and last month stood at just 341 tons, Indonesia's Antara news agency reports.
''I wanted this case to be settled without giving too many political statements. The most important thing is that our goal is achieved … and our people who are affected receive a good compensation,'' said Yudhoyono.
Stressing that he held PTTEP Australasia accountable for the disaster, the president told Cabinet members that the country's relationship with Australia and Thailand wouldn't be strained.