Police in South Australia say they have not seen a "significant increase" in domestic violence reports during the coronavirus pandemic, despite an alleged murder in the state last week and experts' predictions of a rise in incidents.

Key points: There have been increases in domestic violence in other states, Commissioner Grant Stevens said

There have been increases in domestic violence in other states, Commissioner Grant Stevens said Support groups have warned about the impact of lockdowns on vulnerable partners

Support groups have warned about the impact of lockdowns on vulnerable partners South Australia today recorded no new COVID-19 cases for the third day in a row

Commissioner Grant Stevens today said the number of calls regarding domestic violence reports had not spiked since coronavirus response measures were introduced in South Australia.

"We were closely watching, but at this point in time haven't seen any sort of significant increase in … domestic violence," he told ABC Radio Adelaide.

"Internationally, and interstate, there have been some trends that show an increase in domestic violence offences.

"But I think we're more balanced here in terms of the level of restrictions we have, which means people still have some freedom to get out and about and spend time on their own and away from people they're concerned about."

Commissioner Stevens' comments came less than a week after a woman in her 30s was allegedly murdered in her home in Adelaide's southern suburbs by her former partner.

Commissioner Stevens suggested SA's "more balanced" restrictions allowed people to get outdoors and away from others. ( ABC News: Nick Harmsen )

Police and paramedics were called to the Morphett Vale house around 12:30pm on Thursday, where they found the woman's body.

Police said neighbours living near the woman's house did not contact emergency services despite hearing a cry for help.

A man described by police as the woman's former partner was arrested and charged with murder on Thursday night, and the man has since appeared in court where his identity was suppressed.

In recent weeks, anti-domestic violence campaigners warned of a predicted rise in incidents, with more victims effectively trapped inside their homes alone with abusers for long periods of time.

Interstate, police have reported increases in domestic violence in the last month.

Figures provided to ABC Radio Perth by WA Police, which compared the month of March 2020 to the same period last year, showed domestic violence was increasing, with a five per cent rise in cases.

The Western Australian Government has now set up a COVID-19 family and domestic violence taskforce to work with police and service providers to ensure services remain open during the pandemic.

SA records third day of no new COVID-19 cases

Despite a record number of tests during the state's blitz, Monday marked South Australia's third consecutive day with no new coronavirus cases.

Chief public health officer Nicola Spurrier said nearly 2,000 people were tested on both Thursday and Friday, more than 1,000 on Saturday and 968 on Sunday.

"Thank you to all of those people who have developed the mild cold in the last three or four days and [who have] come forward and had a test done," Dr Spurrier said.

"It's all very reassuring … so keep up the good work."

SA Pathology has now conducted more than 44,000 coronavirus tests since February.

Dr Spurrier (left) has urged South Australians to "keep up the good work" in combatting coronavirus. ( ABC News: Michael Clements )

While she said the results were encouraging, Dr Spurrier urged South Australians to remain vigilant and adhere to the current restrictions.

"We still need to continue all of the things we've put in place, particularly the hygiene and social distancing," she said.

Of the 435 confirmed cases in the state, 85 per cent — or 369 people — have now recovered.

Six people remain in hospital, with two of those receiving treatment in intensive care.

Dr Spurrier said authorities would turn their attention to lifting restrictions in light of the positive results.

"Over the coming weeks we'll certainly be planning, and we're looking to do some very intensive planning, to see what restrictions should be lifted when," she said.

"National Cabinet will be meeting tomorrow and more things will be announced."