Testing stations should remain open around the clock and more should be opened in Adelaide's north to handle a surge in demand because a growing COVID-19 cluster, the South Australian opposition says.
Labor has also called on SA Health to create a dedicated clinic for people urgently being asked to get tested because they may have links to the Parafield outbreak.
"It has been outstanding to see so many South Australians do the right thing and seek to get a COVID-19 test," Opposition Leader Peter Malinauskas said on Wednesday.
"But it has been disturbing to see people, many of them unwell, forced to wait for more than 10 hours, with many turned away.
"It's understandable there would be long queues in the immediate hours following news of this cluster, but it's now been three days."
Mr Malinauskas said the urgency of the situation was even greater with Adelaide forecast to have a top temperature of 34C on Wednesday, meaning many people will spend hours in the heat waiting for a test.
About 5000 people were tested on Monday and more than 6000 on Tuesday with some people forced to wait in line for up to 12 hours and others turned away when centres closed.
So far there's been 20 confirmed coronavirus cases linked to the Parafield cluster but that number is expected to grow.
It was sparked when a cleaner in one of Adelaide's quarantine hotels was infected and passed it on to her family members.
In a social media post on Wednesday, SA Health urged people getting tested to be patient and to expect delays.
It said people attending at walk-in sites should bring water, snacks, sun protection and a chair.
Chief Public Health Officer Nicola Spurrier said officials were aware of the long delays and were working to increase staffing and resources.