SA Health says it is unlikely the woman who sparked the latest NT COVID-19 lockdown was infectious while in the state.
SA Health said the 21-year-old woman drove from Adelaide to Melbourne on October 21 before returning on October 24, then staying overnight in South Australia.
NT Chief Minister Michael Gunner had previously said she arrived in South Australia on October 25.
She later flew to Cairns and Darwin.
SA Health said it was investigating the woman's movements within South Australia but has so far not listed any exposure sites connected with her.
She tested positive in Darwin on Friday night.
"These actions have put the Territory at risk," Mr Gunner said.
"They forced Katherine into lockdown and forced Katherine business to shut.
"While there were compassionate reasons for her decision to visit Victoria, there were not compassionate reasons for lying to the Territory and coming here from a hotspot."
Vaccinated Northern Territory residents can come to South Australia — with testing — but those who have not received a full COVID-19 vaccination course cannot enter the state.
Unvaccinated South Australians can return to the state but have to do 14 days' quarantine
South Australia's double-dose vaccination rate reached 70 per cent today, after another 11,000 jabs were delivered yesterday.
No new COVID-19 cases were reported in South Australia today, the fifth day in a row with no new or active cases.
