An oil company behind allegations that East Timor's former prime minister accepted bribes from oil giant ConocoPhillips, says banking records in Darwin could be destroyed before the case goes to trial.

Oceanic Exploration wants $US10 billion ($A13.4 billion) in damages, for the alleged theft of its oil rights in the Timor Sea. In a case before the US District Court, Oceanic alleges it was granted exclusive rights to oil and gas fields in 1974, but that ConocoPhillips used bribery to steal the rights.

Oceanic specifically claims it paid $US2.5 million ($A3.3 million) to East Timor's former prime minister Mari Alkatiri to award the rights to ConocoPhillips. Oceanic alleges Dr Alkatiri and his family deposited the money in two Darwin banks.

ConocoPhillips denies the allegations and has asked the court for more time to respond. But Oceanic argues under the seven-year rule, the banks may destroy crucial financial records if the case is delayed further.