The party is set to form a minority government with Labor, with Shane Rattenbury comfortably returned, but had lost 0.1 percentage points from their disappointing 2012 result with 76 per cent of the vote counted.

Mr Rattenbury, reflecting the upbeat mood of the party faithful at the Polish Club, said he remained optimistic of gaining another seat once voting had been completed by next Saturday.

"Some of us are going to have a very nervous week, we're on a knife-edge in a couple of seats," he said. "We're definitely in it. In light of all the negative attacks, I'd be very pleased with any increase in numbers," he said.

The most likely second MLA, Caroline Le Couteur in Murrumbidgee, speaking about 8.30pm, said she was "excited" but no more than hopeful of her chances. The Greens had 0.7 of a quota in the Woden-Weston seat late on Saturday night. They had 0.6 of a quota in Ginninderra at the same time.

"I was elected in 2008 on 0.5 quota, but I have seen enough elections to only be hopeful," she said.

Mr Rattenbury received a call from Chief Minister Andrew Barr about 9.20pm where he was told Liberal leader Jeremy Hanson had conceded, and welcomed the "rejection of the negativity" of the Canberra Liberals.

"I'm excited for Canberra," he said. "There was a clear divide in policy, and I'm so grateful they backed us."

However, he acknowledged the light rail issue had not been an electoral positive for the party in all regions.

"It has been an incredibly polarising election, and the Liberals have sought to make a great deal of light rail in particular, and the area we've struggled the most, in Brindabella, is where that issue has been particularly heavily paid out," he said.

"We have been mercifully attacked by the clubs industry, by the poker machine lobby, and by the Liberal Party, so in that context it has been a challenging election for us."

Ms Le Couteur, 64, had earlier told party supporters at the Polish Club "we're back", which she later explained to be in contrast to the 2012 result, where three Greens MLAs lost their seats.

"The atmosphere is different," she said. "Clearly we had lost MLAs, this time we haven't lost MLAs."

Mr Rattenbury had earned 0.8 of a quota on his own in the central seat of Kurrajong late on Saturday, behind only Mr Barr in the seat, who had 1.3 quotas. The Greens overall had 1.2 quotas in the seat.

Mr Rattenbury, who held four portfolios including education before the vote, said questions of whether he would be part of the ministry or what role he would play on a crossbench would be discussed once all results were known.

Ms Le Couteur, the executive director of the Australasian Centre for Corporate Responsibility, was the only one of the three Greens MLAs defeated in 2012 who recontested.

She said she had hoped to do a little better in Murrumbidgee, as the party's campaign was the best she had been a part of.

"We have run, compared to the past, an incredible campaign, regardless of the results," she said.