The Welsh Government said it is "on track" to launch its test and trace system from Monday after recruiting 600 staff as contact tracers.
Contact tracing means testing people for coronavirus, tracking the spread, then tracing the people an infected person has come into contact with.
Chief executive of NHS Wales Dr Andrew Goodall said a total of 1,000 tracers will be needed as demand increases, with many of those working in public services.
Scotland has also launched its 'test and protect' system as First Minister Nicola Sturgeon announced an easing of some lockdown restrictions from Friday.
Northern Ireland has already rolled out its own tracing programme.
In the Welsh Government press conference on Wednesday, Dr Andrew Goodall denied that Wales is "behind the curve".
He said: "I think we've been clear about the dates that we've been aiming for.
"We are tracking our normal public health surveillance mechanisms, so our ability to make sure that we've been able to keep an overview of the community transmission rates across Wales.
"We also need to remember that the testing approach is part of the set of measures that we've put in place, it's really important to make sure that we still have the ongoing efforts on the ground."
Dr Goodall said he does not believe those non-compliant with contact tracing procedures should be fined, but said the Welsh Government may review the need to introduce them in future.
There have been contact tracing pilots running in Hywel Dda, Powys, Betsi Cadwaladr and Cwum Taf Morgannwg health board areas since 18 May.
Health Minister Vaughan Gething said the 'test, trace, protect' strategy will be a "key enabler" when Wales seeks to ease lockdown restrictions.
Dr Goodall said there are currently 44 people being treated in critical care for coronavirus - the lowest number since 27 March.
He added more than 62 per cent of critical beds in Wales are empty and available for use.
"There are more than 1,000 people in hospital with coronavirus," Dr Goodall said.
"This includes about 300 people who are on what we call a 'recovery pathway' - they have been treated and are now recovering from the virus in hospital."
Watch Wednesday's Welsh Government press conference here: