The drawnout dispute raises doubts about Jakarta's ability to resolve disputes with foreign investors and the state-owned petroleum firm's capacity for cooperating with oil majors.
Pertamina chief executive Widya Purnama told reporters on Friday that the company would ask president Susilo Bambang Yudhoyono to intervene in the dispute, reported the Dow Jones Newswires and Australia’s Financial Review.
"[Yudhoyono] was the one who wanted a joint operation for Cepu," Purnama said.
The Yudhoyono government had promised to resolve the wrangle when it came to power in 2004.
The four-year dispute had appeared close to resolution, after the companies signed a 30-year production-sharing contract in September.
But Exxon insists on being the sole operator for the project, while Pertamina wants the two companies to operate the block in five-year rotations.
Purnama said his company refused to hold further meetings with Exxon.
“Several meetings with Exxon have failed to produce results and always met deadlock,” he said, according to the Financial Review.
Containing estimated reserves of about 600 million barrels of crude oil, Cepu has the potential to rejuvenate Indonesia's flagging oil output.
Indonesia's oil production has fallen in recent years due to a lack of investment in oil exploration and production.