It could be two weeks before the new system for tracking and tracing coronavirus cases is rolled out across Wales, a council leader has said.
The Welsh Government had said it wanted its Test, Trace, Protect (TTP) scheme to be operational by the end of May.
Andrew Morgan, leader of the Welsh Local Government Association (WLGA), suggested the IT system would be ready by "the first or second week of June".
The Welsh Government said the aim was to roll it out from the start of June.
TTP involves tracing anyone who has come into close contact with someone who has tested positive for Covid-19 and advising them to self-isolate to stop further spread.
The Welsh Government's lockdown exit plan made clear TTP's success was central to making the easing of lockdown measures possible.
Last week, the WLGA leader said setting up the system in Wales was a "mammoth" task and councils would need "significant additional resources" for the "vital" work.
On Friday, First Minister Mark Drakeford said it was an important weekend for the development of the contact tracing system with four "small scale" trials "continuing at pace" in Cwm Taf Morgannwg, Powys, Betsi Cadwaladr and Hywel Dda health board areas.
Staff from six councils - Bridgend, Merthyr Tydfil, Rhondda Cynon Taf, Ceredigion, Powys and Anglesey - are also involved in the trials.
Speaking on the BBC Politics Wales programme, Councillor Morgan, who is also leader of Rhondda Cynon Taf council, said: "The pilots are going reasonably well so far, but this is about a learning exercise before the full Wales-wide roll-out.
"I understand the IT platform which supports all this will be in place around the first or second week of June.
"Once that's in place, we'll have a complete link up across all local authorities, all local health boards."
About 1,000 staff will be needed in the early stages of the system with the majority of the workforce redeployed by councils from their usual jobs.
The system requires an increase in testing capacity for those in hospital, care homes and key workers to about 10,000 by the end of the month.
On 17 May, there was laboratory capacity in Wales to conduct 5,330 daily tests.
Despite joining a UK-wide testing system earlier in the week, concerns have been raised that people in Wales are still not able to book drive-through coronavirus tests.
In England, Scotland and Northern Ireland members of the public are able to book drive-through tests online.
Home test kits are available to anyone over the age of five across the UK showing coronavirus symptoms, but availability depends on demand.
The Welsh Government said an update on home testing kits would be provided as "soon as possible".
Councillor Sam Rowlands, Conservative leader of Conwy council, said: "Many of us have been concerned at the slow response in terms of the mass testing here in Wales, and particularly in care homes and suchlike.
"For my area the average speed of results coming back is around 72 hours, and I've seen examples where it's taken five or six days."
The Plaid Cymru leader of Ceredigion Council, Councillor Ellen ap Gwynn, said: "We've been working very closely with the health board here [Hywel Dda}, and our testing regime works through them.
"It does seem to be working more efficiently than the tests that have to go down to the lab in Cardiff...
"What we need all over Wales is more locally-based testing facilities where we can get that quick turnaround - otherwise things won't work as well as they should."
A Welsh Government spokesman said: "Contact tracing trials are ongoing in four areas across Wales. We aim to roll this out across Wales from the beginning of June.
"The contact management system that will allow all local authorities to record their data in one place will go live from the end of the first week."
- Dinas Powys
- Merthyr Tydfil County Borough Council
- Merthyr Tydfil
- Rhondda Cynon Taf County Borough Council
- Coronavirus pandemic
- Coronavirus testing
- Cwm Taf Morgannwg University Health Board
- Bridgend County Borough Council
- Ceredigion County Council
- Welsh government
- Powys Council
- Isle of Anglesey County Council
- Conwy County Borough Council