Scores of cars and people were seen lined up for blocks at the handful of testing clinics around Wollongong on Wednesday, after a second positive case of COVID-19 was uncovered.

Cr Bradbery praised the efforts by NSW Health and the community for their quick action, but said the response from people to get tested was "overwhelming" on the system.

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"Council has indicated we're prepared to make available quite a few community facilities if required, we're not holding back in making options available [for COVID-19 testing]," he told the Mercury.

"I think the challenge was for NSW Health to mobilise this so fast and also to find the resourcing and staffing of these testing centres."

Cr Bradbery was optimistic NSW could "get on top of it" though urged all Illawarra residents - and people across the state - to stay at home and not to travel.

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"That should have been one of the calls, that people limit their movements while this current outbreak is being managed," he said.

"It's quite feasible for someone in Wollongong to go to a large gathering or event on the other side of Windang bridge."

As of Wednesday, restrictions for Wollongong and Greater Sydney household gatherings were limited to five visitors including children; and the limit for outdoor gatherings reduced from 50 to 30.

Shellharbour and Kiama could host up to 50 visitors from any number of households at any one time.

Shellharbour Mayor Marianne Saliba said travel within the Illawarra was concerning, especially due to the large Greek population in her locality which may have visited the two Wollongong churches at the same time as one of the positive COVID cases.

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"If there's someone who has tested positive in Wollongong there is every likelihood they could have been in Shellharbour or have family members in Shellharbour," she said.

While she said extending the reach of pandemic restrictions was not the answer, Cr Saliba urged people to keep their hygiene up and follow the public health orders.

"It's up to every individual to understand the responsibility that they have," she said.

"If they feel unwell get tested, if they've been to any of the sites identified [by NSW Health] get tested, maintain physical distance and ensure they look after their personal hygiene to do everything we can to stop the spread."

It comes as Labor's health spokesman and Member for Keira Ryan Park called for mandatory mask wearing at churches, shopping centres and on public transport across NSW.

He said the Wollongong cases of COVID-19 showed these three areas were "difficult to ensure social distancing".

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