Secondary schools in Swansea and Neath Port Talbot will be targeted in another round of school MMR vaccinations this week.
Over 1,700 pupils will be offered the jab in 10 schools across the areas.
Health experts have urged parents of pupils who have had no MMR or who need a second jab to take advantage of the school clinics.
Around 3,400 people turned out to receive the MMR vaccination in the latest round of clinics in South Wales over the weekend.
Health chiefs at Abertawe Bro Morgannwg University Health Board say 1,800 people were vaccinated at the area's four drop-in MMR clinics today – the highest number so far.
The full numbers are:
- Princess of Wales Hospital: 727
- Neath Port Talbot Hospital: 455
- Morriston Hospital: 341
- Singleton Hospital: 302
Many of the 1,825 given MMR jabs were older schoolchildren, teenagers and young adults - the target age group for vaccines.
Dr Marion Lyons of Public Health Wales says with 20 new cases of measles daily in Wales at the moment a death would not be surprising.
An investigation is underway on Friday to find out if a 25 year-old man from Port Tennant near Swansea died from the virus.
It is reported that a 25 year old man found dead at a flat on Port Tennant Road in Swansea yesterday died from 'suspected' measles.
South Wales Police have confirmed that the death is not being treated as suspicious and that officers are awaiting the results of a post mortem examination.
Public Health Wales have told ITV News that they will be releasing a statement 'shortly.'
Public Health Wales says vaccinations are being offered to parents in Swansea "on a scale never seen before."
It says the measles virus has continued to circulate and spread among children in the easter holidays, and is expected to spread further among those susceptible now they are back at school.
Public Health Wales says there are now cases of measles in every health board area in Wales.
Dr Marion Lyons, Director of Health Protection, says "we have no way of knowing where the outbreak might spread."
Public Health Wales says the number of cases in the measles outbreak has reached 765.
An extra 72 cases have been reported since Thursday.
A total of 77 people have now been hospitalised during the outbreak.
Wales' Health Minister says he "remains concerned" about the measles outbreak, and anticipates that the number of cases "will continue to rise over the coming weeks."
In a written statement, Mark Drakeford reiterated the calls of public health officials for as many people as possible to have MMR vaccinations.
Abertawe Bro Morgannwg Health Board begins vaccination clinics in schools in Swansea tomorrow, and Mr Drakeford said other health boards will also be offering catch-up clinics targeting schools with low vaccine uptake.
He said: "The Welsh Government, Public Health Wales and the Health Boards will continue to take all necessary and appropriate measures to reduce the impact of the outbreak as far as possible."
The latest figures on the number of cases in the outbreak are due later today. Last week they reached 693.
Firgures from Abertawe Bro Morgannwg University Health Board show that more than 10% of children aged 11 to 16 in Swansea have not had both MMR vaccinations.
The number of children unvaccinated in Monmouthshire are also higher than the all-Wales average. More than 15% of children aged between 11 and 18 years old have not received both MMR vaccines.
More children in Powys, Newport, Ceredigion and Pembrokeshire have unvaccinated than the national average.
Public Health Wales have published more details of the number of cases of measles in an outbreak centred on Swansea.
The data shows that the number of cases has risen rapidly in February and March.
It also shows that children aged between 10 and 14 years old are the most at risk.