More than 1,800 people have attended drop-in MMR clinics at four hospitals in Swansea and Neath Port Talbot, as the death of man linked to the measles outbreak is investigated.
Gareth Williams, 25, died at his home in Swansea on Thursday.
Tests by Public Health Wales have confirmed that he had measles at the time of his death.
The number of reported measles cases in Wales now stands at 808.
It is the third weekend in a row that vaccination clinics have been held, in a bid to stem the epidemic.
"We're seeing older people today - more teenagers and adults, which is great," said Dr Sara Hayes, director of public health for Abertawe Bro Morgannwg Health Board (AMBU).
"The message from me is if you were born after 1970 and you haven't had a measles or two MMRs, you should come for a vaccination if you live in our area."
Pupils at five schools have also been offered MMR jabs, with a further 10 schools being visited by vaccination teams in the coming week.
The appeal by PHW for parents to make sure their children are vaccinated against measles has taken an increasingly urgent tone, following the death of Mr Williams at his home in Port Tennant Road in Swansea.
Tests on Friday confirmed that Mr Williams did have the disease when he died, though further investigations are under way to establish if the illness is linked to the death.
"Whatever the cause of death in this case we should not be surprised if, as the outbreak grows, we start to see deaths in Wales," said Dr Marion Lyons, PHW's director of health protection.
"Those not fully vaccinated with two doses of MMR are highly likely to catch measles, which is highly contagious."
"We know that there are unprotected people in all age groups but we have particular concerns about the 10 to 18 age group."
Since the outbreak began in November, 77 people have needed hospital treatment for the illness.
Health officials said 1,825 had been seen at four hospitals in Bridgend, Swansea and Neath Port Talbot on Saturday.
The breakdown of people vaccinated were:
- Morriston Hospital, Swansea 341
- Singleton Hospital, Swansea 302
- Princess of Wales Hospital, Bridgend 727
- Neath Port Talbot Hospital 455
One woman from Port Talbot, who took her teenage daughter in to be vaccinated, said: "Get it done. Especially with the outcome of the last week, people are very sick because of it then I think we should get vaccinated."
Another mother, of a toddler, said: "My daughter had her routine injection when she should have at 13 months but I decided to come down and give her the second dose earlier - better to be safe than sorry."
A fourth round of clinics will also be held next Saturday, again at the four main hospitals in the Swansea area.
Meanwhile, Aneurin Bevan Health Board said 1,600 vaccinations were carried out at three hospitals in Newport, Abergavenny and Ystrad Mynach at special clinics on Saturday.
The health board has reported 36 measles cases so far this month, mostly in the Caerphilly and Newport areas.
PHW has been urging parents of children across Wales to ensure they have been vaccinated, warning that there are cases of measles in every single health board area.
The call has been backed by the Betsi Cadwaladr University Health Board covering north Wales, who warned that the outbreak in south West Wales is likely to spread to other areas.
It follows an outbreak that affected 60 people in the Porthmadog area in 2012.
"The likelihood that unvaccinated children across the country will come into contact with those already infected is high," said Siobhan Jones, a consultant in public health at the Betsi Cadwaladr board.
"It is vital that parents act now to ensure that their children are fully immunised with the MMR vaccine."