The fate of East Timor's next government could be decided by a judge, with Fretilin arguing it has the constitutional right to appoint the prime minister.
The party refuses to rule out a legal battle should President Jose Ramos Horta challenge its authority.
The constitution states that the president appoints the prime minister, who 'shall be designated by the most-voted political party or alliance of political parties with parliamentary majority'.
Most observers read that as giving Mr Ramos Horta the right to choose the prime minister, in the wake of last week's elections that left no clear winner. They say Mr Ramos Horta is free to pick former resistance leader Xanana Gusmao, whose National Congress for the Reconstruction of East Timor came second at the polls with 23 per cent of the votes.
The congress has since joined forces with three other parties, and controls 37 of the next Parliament's 65 seats.
But legal experts in Fretilin argue the party should be given the mandate as it won 29 per cent of the vote.
'The 'parliamentary majority' in section 106 [of the constitution] does not refer to an absolute majority,' said a statement from lawyers Sahe Da Silva and Jose Teixeira, who are Fretilin members.
'The reading of the constitution means that only Fretilin, as the 'most-voted' political party, can appoint the prime minister.' Fretilin, which is slated to have 21 seats in the new Parliament, says it wants to form a minority government.
Mr Teixeira, who was natural resources minister, said the congress-led coalition did not have the legal right to govern as it was established after the election. 'In parliamentary elections, people do not vote for a coalition that has yet to come into existence,' he said.
Officially, Fretilin is sitting on the fence, saying 'the party is confident that President Jose Ramos Horta will act constitutionally, so we are not yet contemplating any next move'.
But Mr Teixeira has already made it known that Fretilin is not likely to take an unfavourable decision lightly. 'We have our constitutional rights and we are prepared to pursue all avenues to have them respected.'
Warren Wright, publisher of East Timor Law Journal, said Fretilin's argument was groundless. 'The argument is based on a flawed juridical analysis of the constitution. The 'most-voted party' would only apply if there were no coalition commanding a majority,' said the lawyer, who has an in-depth knowledge of East Timor's legal system.
'Also, the assertion that any such alliance must have been formed before the election is utter nonsense. The constitution does not require that and the election law cannot override the clear provisions of the constitution.'