Around 2,500 people have been vaccinated at clinics set up to tackle the Swansea measles epidemic as fears were raised it could spread.
Queues of people turned up early at many of the special drop-in sessions for free MMR jabs.
The number of cases in the outbreak has risen to 693 but Dr Meirion Evans of Public Health Wales (PHW) said that numbers could "easily double".
He said 40,000 children in Wales remain unvaccinated.
Dr Evans said that the epidemic centred around Swansea is a result of a 10 to 15 year "legacy" of concern about the MMR (measles mumps rubella) jab.
It followed a now discredited report by Dr Andrew Wakefield in the late 1990s which linked the vaccine with autism.
Dr Evans, a consultant epidemiologist, told BBC Radio Wales that as a result, there are many parts of the UK which do not have vaccination rates high enough to stop the spread of measles.
"Across Wales as a whole there are many, many children who have not had their MMR - we estimate over 40,000 children across Wales - so there is a real possibility that it could seed from Swansea to other parts of Wales and potentially take a grip there," he said.
"Nowhere in Wales is safe from measles and I think that is true of the UK as a whole."
He warned that the outbreak could last until the summer holidays as the disease can spread rapidly in schools.
On Saturday, special clinics were again held at hospitals across south Wales to try to vaccinate as many people as possible, with two more health boards taking action.
More than 1,700 people had the MMR jab at the drop-in sessions at Morriston and Singleton Hospitals in Swansea, along with Neath Port Talbot Hospital and the Princess of Wales Hospital in Bridgend.
Abertawe Bro Morgannwg University Health Board said many clinics opened earlier than the intended 10:00 BST start time as people began queuing as early as 08:30 BST.
A similar number attended clinics at the same hospitals last weekend, and more drop-in sessions will be held next weekend, the health board added.
In south east Wales, 400 people received the vaccine in Ystrad Mynach near Caerphilly and 200 people had the jabs in Newport in sessions arranged by the Aneurin Bevan health board.
Meanwhile around 200 people attended clinics at Cardiff Royal Infirmary and Llandough Hospital near Penarth.
Dr Tom Porter, a consultant with Cardiff and Vale University Health Board, said that while there was not yet an outbreak in the area, doctors were seeing cases imported from elsewhere in Wales.
"It's probably a matter of sooner or later seeing significant spread within Cardiff and the Vale of Glamorgan," he added.
"We know at the moment not enough people are protected from measles which means probably we will get an outbreak and we want to make sure enough people are protected."
He added that an estimated 13,000 children under 19 have not had both recommended MMR jabs in the Cardiff and Vale area.
Cwm Taf Health Board in the south Wales valleys has not held any drop-in sessions but has advised people to contact their GP for a vaccination.
PHW has warned that despite previous immunisations the outbreak, which began in November, has not been brought under control.
Although the epidemic is based in Swansea, cases continue to be reported across Wales. Officials have raised concerns about the number of cases in Powys.
Measles is caused by a virus spread in droplets and is easy to catch by those who have not been vaccinated.
Typical symptoms of measles include fever, cough, conjunctivitis and a rash. Complications are quite common even in healthy people, and about 20% of reported measles cases experience one or more complication.
The death rate is around one in every 1,000 infected in developed countries.