Labor set to make big gains in Senate but Albanese says government 'not getting carried away' with mandate

Labor will have a far friendlier Senate to work with this parliament in a major boost to its hopes of implementing the policy platform it took to the election, while Jacqui Lambie is in a tight race to retain he seat.

While upper house results take weeks to be finalised, the early counting indicates the Albanese government will pick up at least two seats: one in South Australia and one in Queensland.

It could also make gains in NSW, Victoria, and Western Australia, with Labor candidates currently leading the race to claim the final available seat in each of those states, although more than 50 per cent of the vote remains to be counted.

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Even without any of those three, the two extras already as good as confirmed would give Labor 27 seats, leaving it needing to find 12 extra votes to pass legislation.

The Greens have had a far better election in the Senate than the House of Representatives – it looks likely to retain all of its upper house seats, even as it's been reduced from four to as little as one in the lower house.

That result would leave Labor only needing to negotiate with the Greens and one other independent to pass legislation if it is opposed by the Coalition.

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That could come in the form of David Pocock, who comfortably retained his ACT seat with a greater vote than senior Labor senator Katy Gallagher, ALP-turned-independent Fatima Payman, or Jacqui Lambie – although she is far from certain to win Tasmania's last Senate opening.

Should Labor win 28 seats or more, it would only need the support of the Greens to pass its bills.

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Despite the increase in the Senate, Prime Minister Anthony Albanese said he wouldn't be going beyond the mandate handed to his party in Saturday's crushing election win.

"We're not getting carried away," he told reporters.

"We've been an orderly government.

"The thing I reject is we haven't been ambitious. Look at our agenda on the clean energy economy, on child care, on gender equality, on education... we won't get carried away and we'll continue to engage."

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One of the senators he flagged talking to was Lambie, even though she is in a close fight to retain her seat.

"One of the conversations I have had is with Jacqui Lambie," Albanese said.

"In Tasmania, her result is still a little bit unclear, but she's someone I respect.

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"On [veterans] affairs, I will talk to Jacqui Lambie every day of the week, whether she's in the Senate or not."

One Nation's Malcolm Roberts is in a similar battle for his seat in Queensland as Lambie is in Tasmania, with Legalise Cannabis and ex-LNP senator Gerrard Rennick also in contention.

One Nation could also gain a seat in Western Australia, where it is battling Labor for the last upper house spot.

In the Northern Territory, Labor incumbent Malarndirri McCarthy and Country Liberal counterpart Jacinta Nampijinpa Price will retain their seats.

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