Independent candidate Andrew Wilkie has claimed victory in the seat of Denison in Tasmania.
But he says he will wait a few more days before declaring who he will support in a hung parliament.
Mr Wilkie on Saturday joined Prime Minister Julia Gillard in Melbourne for their first formal meeting, in which he presented her with a list of about 20 issues he wants addressed by the new government. They will meet again on Monday.
The ABC reports the support of Mr Wilkie is vital for Ms Gillard, whose Labor Party has 72 seats in the new Parliament, four short of the number needed to govern.
Mr Wilkie will hold the balance of power in the parliament along with Tony Windsor, Rob Oakeshott and Bob Katter.
But he has again distanced himself from the other three other and urged them to decide soon which party they would support in a minority government.
They have requested access to economic advice normally reserved for an incoming government and want to examine Treasury's assessment of Labor and the Coalition's election promises.
Mr Wilkie says he will make his decision in the coming days, after his second meeting with the prime minister.
The former intelligence analyst, who will also meet Opposition Leader Tony Abbott on Monday, has previously expressed his dissatisfaction with both major parties.
"People are sick to death with the behaviour of the Labor Party and the Liberal Party," he has said in light of the election result.
"The problem both parties have got at the moment is I'm unimpressed with both of them."