A union is calling for an investigation into why some coronavirus tests are being processed slower than others.
Less than a third of test results from community testing units (CTUs) came back within 24 hours last week.
The Royal College of Nursing said the data suggested CTUs - mostly used by health care staff - produce results slower than those from hospitals or regional testing centres.
The Welsh Government said it was working to improve turnaround times.
Experts have told ministers that contact tracing schemes "perceived to be most successful" require test results within 24 hours.
Successful contact tracing is seen as central to maintaining the easing of lockdown.
Of the 8,664 tests done at CTUs last week 32% came back in 24 hours, and 49% in 48 hours.
The 11 regional drive-through centres which are mostly used by the general public performed better, with 39% of their 5,520 tests coming back within 24 hours, and 83% in 48 hours.
Tests done in hospitals were the quickest where 80% of the 5,613 tests came back in 24 hours, and 96% within 48 hours.
Since mid-May there has not been a single week when CTUs processed more than half their tests within 24 hours.
Helen Whyley, director of the Royal College of Nursing in Wales, said: "In the last four weeks it appears that there are much slower test results coming out of the community testing units."
"The data seems to suggest that it is taking longer to get results when individuals are tested in the community compared with regional centres and hospitals.
"This could be a very significant issue moving forward and we would urge the Welsh Government to investigate this and put it right as a matter of priority."
Welsh Conservative health spokesman Andrew RT Davies said the proportion of CTU results coming back within 24 hours was "simply not good enough".
"The coronavirus testing regime in Wales has been an abject failure and Welsh Labour's health minister needs to get on top of the situation urgently," he said.
"If he can't, or his priorities are elsewhere, then he should appoint someone who can."
Plaid Cymru health spokesman Rhun ap Iorwerth said the situation was "very worrying".
"We need to know why and what can be done to speed things up," he said.
"Quick turnaround is the first piece of the jigsaw in many ways - that's how the alarm bell is rung promptly and it's what triggers the all-important contact tracing and isolation to stop further transmission."
First Minister Mark Drakeford has said he wants to "simplify and accelerate" the system.
On Sunday he told the BBC's Politics Wales programme he wanted faster turnaround times "so when there are greater volumes of tests needed we will be in a better position than we have been over the last month".
And in the Senedd last week Mr Drakeford said an "enhanced courier service" was being arranged to ensure tests are taken to laboratories "more quickly and more regularly".
A Welsh Government spokesman said: "We are working with partners to improve turnaround times.
"Turnaround times for CTUs are a key focus of this work."