While Liberal gains in key seats have dampened Labor's hopes for a majority government, the interim Minns ministry took the reins of government at a small ceremony at Government House on Tuesday.

A handful of close family and staffers were there to witness Governor Margaret Beazley urge the eight MPs to savour the "unique moment" in their lives.

The enormity of the occasion showed on the 43-year-old premier's face as he raised his eyebrows at wife Anna after taking his oath.

"We don't know the final composition of the next parliament but my team and I are ready to hit the ground running," he later told reporters.

"We know there's a huge responsibility on our shoulders and work starts today."

Ms Car became the second woman to become deputy NSW premier after Carmel Tebbutt, while also taking the education and early learning portfolio.

Daniel Mookhey is treasurer, former opposition leader Michael Daley is attorney-general, Jo Haylen has the transport portfolio while Penny Sharpe is environment and heritage minister.

Ryan Park is health minister while John Graham has responsibility for roads, arts, and is special minister of state.

The full ministry is expected to be sworn in next week once the parliament's final make-up is clear.

Labor needs 47 seats to have a lower house majority but was stuck on 45 on Tuesday morning as the coalition pushed ahead in eight of the seats still in doubt.

Liberal candidates leapfrogged Labor's early leads in Goulburn, Terrigal, Winston Hills, Holsworthy and Miranda on Monday.

Labor's lead in Kiama is also slipping away with the seat likely to fall to independent Gareth Ward on Tuesday, according to the ABC's chief election analyst Antony Green.

"All the inside information I have says that Gareth Ward will win Kiama so Labor can't reach a majority," he tweeted.

Mr Ward, a former Liberal minister, was dumped from the party and suspended from parliament last year after being charged with historical sexual and indecent assault offences.

As counting continues in the tightly-contested race, Mr Ward pleaded not guilty in Nowra District Court on Tuesday to five charges.

Another potential seat was shaved from Labor's column late on Monday, as the party's candidate for Balmain Philippa Scott conceded to new Greens MP Kobi Shetty.

Labor remains about 230 votes ahead as counting continues in Ryde.

The swearing-in ceremony allows for departments to start formally briefing the state's first Labor government in 12 years.

Early priorities are the Menindee fish kills, the northern NSW flood recovery and transport issues that have caused repeated delays on the state's train network.

The new premier spent two hours in a briefing with former premier Dominic Perrottet on Monday as the pair continue their friendly relationship.

Later, Mr Minns made a midnight visit to Sydney's Westmead Hospital, where he met with nurses and paramedics working the overnight shift.

He also visited the children's ward, leaving notes for children to give to their teachers, saying they did not have to do their homework because they were sick.

After Mr Perrottet's resignation as Liberal leader, former planning minister Anthony Roberts, former attorney-general Mark Speakman, and former trade minister Alister Henskens have emerged as leading contenders for the vacant Liberal Party leadership.

Moderates Matt Kean and James Griffin have bowed out of the race.

The incoming government was given a political boost when a trio of independents - Alex Greenwich, Greg Piper and Joe McGirr - promised confidence and supply, if Labor cannot form a majority.

Early counts show Labor will win eight seats in the upper house, the coalition six, the Greens two, and one seat for One Nation.

Remaining votes and preference flows will decide the last four seats that were up for election.

Australian Associated Press