Mr Malinauskas was sworn in as Premier on Monday after Labor's decisive state election victory.

Susan Close was also sworn in as his deputy and Stephen Mullighan as the new treasurer.

The premier confirmed on Tuesday that the rest of the cabinet would take up their roles from Thursday at the same time confirming Christ Picton would be the health minister.

Mr Picton took part in briefings the premier had on Monday with the state's chief public health officer and other officials on the latest situation with the COVID-19 pandemic.

Mr Malinauskas is expected to retain most of his opposition frontbench team in his first ministry but said there would be some minor movements.

"We've been working incredibly hard to ensure it's the best cabinet that my government can offer," the premier said.

"There will be some changes, they won't be major, but there will be some changes to both portfolios and personnel."

The premier's comments came as counting continued after Saturday's poll.

Labor now seems certain to hold at least 26 seats in the 47-seat House of Assembly and is strongly favoured to pick up one more.

But its chances of tipping out former premier Steven Marshall in Dunstan appear to be fading with the party's lead there shrinking from 143 votes late on Monday to just 11 as counting of pre-poll and postal ballots continued.

Those early votes were expected to continue to favour Mr Marshall.

With Dunstan, the Liberals are likely to hold 14 or 15 seats with five or six going to independents.

Dan Cregan in the Adelaide Hills, Geoff Brock, who shifted to the seat of Stuart in the mid-north, Troy Bell in Mt Gambier and Fraser Ellis in Narungga, which takes in Yorke Peninsula, have all been returned.

In Finniss, independent Lou Nicholson and Labor's Amy Hueppauff were locked in a tight battle to unseat former primary industries minister David Basham after he was on the wrong end of a 19 per cent swing.

While in Hammond sitting Liberal Adrian Pederick was struggling to hold off a challenge from former international soccer referee and local councillor Airlie Keen.

Australian Associated Press