Concerned members of the public have been flocking to two new mobile Covid-19 test centres set-up in Wrexham.
Health officials have said they are dealing with up to 70 confirmed infections at Wrexham Maelor Hospital.
All five deaths recorded in Wales on Wednesday were in the Wrexham authority area.
The Welsh Government has said it could step in "as a last resort" to enforce extra measures to reduce infections.
A further 15 cases of Covid-19 were confirmed in Wrexham on Wednesday by Public Health Wales (PHW).
It represents nearly half of the 32 cases reported across Wales in the last 24 hours.
PHW figures show there have been 57 cases of Covid-19 recorded in the Wrexham area in the last week, which represents 38% of all the cases in Wales over that period.
Health chiefs have linked the increase in cases in the area to both Wrexham's hospital, and to an outbreak at a food processing plant in the town.
Betsi Cadwaladr University Health Board has also confirmed there has been a "small number of confirmed cases" at Chirk Hospital in Wrexham county, and at Deeside Community Hospital and Mold Community Hospital in Flintshire.
The health board's executive director of nursing Gill Harris said "proactive" measures were being taken to prevent transmission at its hospital sites.
She said they had "instigated universal screening for all patients on wards where we may or have had a Covid-19 positive patient".
Patients, visitors and staff at NHS sites across north Wales are also being "actively encouraged" to wear face masks.
David Fearnley, health board executive medical director, said restrictions were being put in place to "get on top of the outbreak" at Wrexham Maelor Hospital, such as reducing patients' movement on-site while undergoing treatment.
"What we want to do is minimise and stop any further transmission," he said.
The two new mobile testing sites are being operated by the Army at the Caia Park Health Centre, on Prince Charles Road, and at the Hightown Community Resource Centre on Fusilier Way.
Health officials said the locations were chosen based on track and trace intelligence gathered in the town.
It also follows the outbreak at Rowan Foods on the Wrexham Industrial Estate, which saw nearly 300 cases of coronavirus since April.
Chief Medical Officer for Wales, Dr Frank Atherton, told BBC Wales earlier in the week there appeared to be transmission in the community, and it also seemed to be linked to more disadvantaged areas in the town.
North Wales Senedd member Llyr Gruffydd said the emerging picture had been "very worrying".
The Plaid Cymru MS has called for all patients and all staff to be tested "not just the ones on affected wards".
The Conservatives health spokesman in the Senedd, Andrew RT Davies, added: "Concern is clearly mounting amongst the public in Wrexham with reports of significant numbers visiting mobile testing centres.
"Local people are understandably worried and this concern is being compounded by the lack of visible communication and leadership from the Welsh Labour Government in Cardiff Bay."
'We are monitoring the situation'
A Welsh Government official told the Local Democracy Reporting Service that it was prepared to step in, but only if all other attempts to stem the virus fell short.
"Action to contain any spread will always be taken at the most local level possible and any national direction would always be a last resort," said a spokesman.
"Outbreak control teams, made up of all key local partners, are carrying out contact tracing and infection prevention and control measures.
"Extra testing is also being co-ordinated at a local level. We are monitoring the situation and will take extra measures if needed."