An update of the vote count from the Australian Electoral Commission on Monday night shows the coalition now has a lead over Labour in two-party-preferred terms of almost 2000 votes.
The development casts a shadow over Prime Minister Julia Gillard's ability to form government and is almost certain to influence negotiations with independents as both sides of politics try to pull together a minority government.
With 80 per cent of the votes counted, the coalition has now taken a narrow lead of 50.01 per cent compared to 49.99 per cent for Labour. The coalition now leads Labour by just under 2000 votes.
Ms Bishop said it was now clear Labour had lost the election and Ms Gillard had no legitimate claim to govern.
"The facts are these - Labour lost 16 seats at the election, Labour lost its governing majority, Labour lost the election," she told ABC television.
"We hold more seats in the House of Representatives, we hold more Senate seats than Labour so it's hard to see what moral authority, or legitimacy Julia Gillard can now claim to try and seek to govern."
Ms Gillard last week insisted Labour's lead in the two-party-preferred vote meant she had the support of the Australian people.
"It now appears clear that Labour has won the two-party vote," Ms Gillard said the day after the election. "That means the majority of Australians who voted yesterday prefer a Labour government."
The coalition also won the primary vote at the August 21 election.
Ms Bishop said the latest development in terms of the two-party vote had taken away Ms Gillard's "only plank" in terms of claims to government.
"She set the bar and said that it was clear Labour was ahead on the two-party-preferred vote; in fact she said they had won the two-party-preferred vote. Well that is not the case," Ms Bishop said.
However, Ms Bishop conceded the question of which party could form a government would come down to the seats held in the House of Representatives, and which way the independents go.
"It comes down to seats, of course, and that's why you need 76 seats," she said.
"We will have 73 seats. That's why we're negotiating with the independents."
The block of three independents in Rob Oakeshott, Bob Katter and Tony Windsor, as well as Andrew Wilkie, will continue negotiating with both sides of politics over the coming days.