Both sides of politics have claimed vindication from the result. Prime Minster Tony Abbott said it was a repudiation of Labor's negative campaign and Opposition Leader Bill Shorten said it signalled voters are opposed to the government's planned cuts.

Dr Glasson won 47.7 per cent of the two-party preferred vote, to Ms Butler's 52.3 per cent, a near 1 per cent improvement on the result of his contest with Mr Rudd last September.

About 70,000 votes have been counted so far and both sides expect Ms Butler to win, despite the postal votes. But Mr Abbott said the result was just the fourth time in 114 years that there had been a swing towards a federal government in a byelection.

''There is still quite a bit of the vote to count,'' he said. ''Let's see where things end up, but as things stand this was a very good result for Bill Glasson, a very ordinary result for Bill Shorten.''

''And [the poll was] an indicator to the Labor Party that, in the end, people want more than just a scare campaign, because that is all Labor had going into the election.''

Dr Glasson said it would be difficult for him to win but that he ''won't concede until those votes are counted tomorrow [Monday]''.

Mr Shorten said the byelection had been fought by Labor on national issues, including what he said were planned health and education cuts by the government.

''[They were] desperate to turn it into a council byelection,'' he said. ''The voters of Griffith look like they have returned another Labor member of Parliament. It's a healthy sign in our democracy that people aren't standing for Tony Abbott's ruthless agenda of health and education cuts.''

Ms Butler will attend her first meeting of the federal Labor caucus in Canberra on Monday.