Ms Kearney, who will now be the first woman to represent Batman, acknowledged her beaten opponent.

"I want to thank Alex Bhathal for a good, hard fought campaign," Ms Kearney said.

Ms Kearney said she had a big family and wished a "very special St Patrick's Day to everyone".

With Labor leader Bill Shorten by her side, she told her supporters she was now on her way to Canberra and "Labor is on its way to a Shorten government".

Mr Shorten said Saturday's win was just one step in Labor's campaign to take federal government, with a swipe at his opponent, Prime Minster Malcolm Turnbull, for not fielding a candidate in Batman.

"We congratulate Alex Bhathal and the Greens political party because at least they turned up," Mr Shorten said.

"Malcolm Turnbull couldn't even be bothered turning up."

The Greens conceded just before 9.30pm that they had probably lost the byelection.

Leader Richard Di Natale, federal MP Adam Bandt and Ms Bhathal addressed a disappointed crowd.

Dr Di Natale congratulated Ms Kearney and Labor for winning "a tough campaign".

He said the vote had been neck and neck on primaries but preferences from right-wing parties had cost the Greens.

"It looks like we're just going to fall short," Dr Di Natale said.

But he said the Greens also lost Melbourne in a close contest one election before ultimately winning the seat.

Ms Bhathal said it had been a difficult campaign for her and her family, in an implicit acknowledgement of the toll internal and unproven bullying allegations had taken.

She wished Ms Kearney well in Canberra, and said it had been noted by many that regardless of the outcome, Batman would have a strong, progressive woman representing the seat in parliament.

"I know that many of you will be hurting tonight, it was not the result we all wanted but ... we'll go on to fight other fights and keep standing up for what we believe in," Ms Bhathal said.

"Of course we will because we're from Batman, the most progressive seat in the country."

Ms Bhathal would not rule out running for Batman again at the next federal election.

Mr Bandt said that Batman was still one of the most marginal seats in the country and within range for the Greens.

"If it's not this time, we'll get ...in next time," he said.

Earlier, the Greens appeared confident of snatching a second lower house seat from Labor, while Mr Shorten conceded the party was in a tough fight to hold on.

At a post-poll gathering in Preston, Mr Bandt warmed up the excited crowd, telling them he hoped it would be the last time he took to a stage as Australia's only federal lower-house Greens MP.

"Whatever the result, one thing is crystal clear," he said.

"The Greens are on the march everywhere, and never again will parties be able to go to an election thinking that if they beat up on refugees they will win, if they open a new coal mine they will win."

With Greens support strongest in the gentrified southern part of the electorate at 2016's federal election, interest turned to whether Labor could hold off a swing in working-class suburbs such as Reservoir and Bundoora in the seat's north.

Earlier, Labor blitzed voters with 10,000 robo-calls and 2400 texts on Saturday, urging senior citizens to get out and vote, following reports that some older people had received phone calls telling them they didn't have to vote.

Saturday’s vote was the culmination of a torrid few weeks of campaigning, particularly for the Greens whose efforts were hampered by internal sabotage from disgruntled party members.

Labor’s campaign ran more smoothly until the last week when the party had to assure retirees in Batman they were not being targeted by its new policy on dividend income from shares.

Ms Kearney also faced a backlash from sections of Melbourne’s Macedonian community, who were furious after Labor campaign material wrongly labelled a Greek language translation as Macedonian.