In short:

South Australian Liberal leader Vincent Tazia says the debate on abortion is "over" following its loss in the Black by-election.

Mr Tarzia says the debate was a "distraction" and anyone who planned a similar private member's bill moving forward "certainly won't be welcome in the shadow cabinet or cabinet".

What's next?

Officials continue to count votes for the Black by-election.The Electoral Commission of South Australia expects the results tally to be updated on Tuesday.

SA Liberal leader Vincent Tarzia says his party will not re-visit the late-term abortion debate following its by-election loss in Black, warning anyone who introduces a private member's bill on the topic "won't be welcome in the shadow cabinet or in the cabinet".

The Liberals conceded defeat in the seat on Saturday night, while Labor celebrated a win for candidate Alex Dighton.

Mr Tarzia told ABC Radio Adelaide the Liberal party now had no choice but to be "united and ruthlessly disciplined" leading into the next state election in 2026.

He said the bill to amend the state's abortion laws, introduced by Liberal MP Ben Hood and voted down in the upper house last month, had been a "distraction" which would not be revisited under his leadership.

"If you're going to have these debates, if they're to be had early in the cycle that's one thing, but under my leadership we won't be revisiting it," he said. 

"It's done, it's dusted. The debate has been had and that's over.

"I'll make it really clear. If anyone makes a private member's bill like that moving forward, they certainly won't be welcome in the shadow cabinet or in the cabinet."

Both major parties allowed a conscience vote on the private member's bill, meaning that MPs did not need to vote along party lines. 

The bill would have required mothers seeking abortion after 28 weeks to deliver their baby alive.

Mr Tarzia attributed the by-election loss for Liberal candidate Amanda Wilson to several factors, including the "scandal" over former MP David Speirs's arrest which he said "damaged our brand".

"I think voters punished us for it," he said.

He said he was proud of how the Liberal team campaigned for the southern suburbs seat but said he would not be making excuses for the "terrible result".

Electoral officials began counting the more than 10,000 early ballots on Monday afternoon, estimated to represented almost half of the total vote.

The Electoral Commission of South Australia expects the tally to be updated on Tuesday.

Labor currently has a two-party preferred swing of around 13 per cent, while the Liberal party is hopeful it can claw the margin back below 10 points.

SA is the only jurisdiction in the nation that does not allow pre-poll and postal votes to be counted on election night.

Premier Peter Malinauskas said the by-election victory did not mean everything was perfect, and that Labor must "keep getting things done".

"We've got a lot more to do, there are challenges out there we've got to confront," he said.

"The Libs can worry about the Libs. Their state of dysfunction is not what [the] people of South Australia want me to focus on, I've got to focus on the job at hand.