The by-election for the federal seat of Batman was marred by a last-minute scandal on Saturday, with reports elderly voters received phone calls telling them they did not have to vote.

In response, Labor launched a phone call and SMS blitz urging senior voters to attend polling centres.

A campaign spokesman decried the move.

"Lying to elderly people is as low as it gets," he said.

"We're encouraging all Batman residents to ignore these dirty tricks and exercise their right to vote."

The electorate has a high proportion of elderly voters, who are traditionally more supportive of Labor.

Labor has declared victory in the Batman by-election, upsetting the Greens who were the favourites to win the inner-Melbourne seat and have now conceded defeat.

Sorry, this video has expired Labor claims victory in Batman by-election

Former ACTU president Ged Kearney was on track to defeat the Greens' Alex Bhathal, with the ALP winning back voters from the Greens in the southern part of the electorate.

The by-election was triggered by the resignation of David Feeney, who was unable to find documents proving he was not a foreign citizen.

The seat in Melbourne's inner-north takes in trendy suburbs such as Northcote and Clifton Hill, and stretches to Preston and Reservoir further north.

It was once a Labor heartland, but gentrification has changed the demographics of the area.

The Greens campaign focused on Queensland's Adani coal mine project and Australia's refugee policies, however Ms Bhathal told ABC radio housing was the number one concern of voters across the electorate.

The Australian Electoral Commission says more than 16,500 people cast an early vote. ( Supplied: AEC )

Her campaign had been marred by internal party leaks, alleging bullying.

The Australian Electoral Commission says more than 16,500 people cast an early vote, with another 14,500 registering for a postal vote.