The college repeated its support for the MMR childhood vaccination programme and said parents should ensure children have received both vaccine doses by contacting their GP practice.
It said MMR has an 'excellent safety record' and there is 'no reason' why single vaccinations should be re-introduced.
Over 900 cases of measles have now been reported in south Wales and the north east of England in what is now the biggest outbreak for 18 years.
More than 2,600 MMR vaccines have been provided in Swansea in south Wales over the past fortnight, including 900 at GP surgeries. But a further 5,000 children remain unvaccinated in the local area and cases are rising daily.
Health authorities in Wales are currently organising a schools vaccination programme targeting unprotected children. However, a peak in cases is expected to be weeks away.
Officials have linked the outbreak to poor uptake of the MMR vaccine in the early 2000s, following the now discredited claims linking MMR and autism.
RCGP immunisation lead Dr George Kassianos said: 'The RCGP fully supports the childhood immunisation campaign using the MMR vaccine and would encourage parents to have their children vaccinated.
'We cannot allow outbreaks of measles, or mumps, or rubella infection when we have a vaccine with an excellent record in safety, requiring only two doses: the MMR vaccine.'
He said MMR was 'one of the safest and most scrutinised vaccines we have ever had'.
Dr Kassianos said there was no evidence that single vaccines provide any advantage to children. The six injections required - versus just two for MMR - could affect the numbers completing their course and put them at higher risk of measles, mumps or rubella, he said.
He added: 'The RCGP urges all parents whose children have not had two doses of the MMR vaccine, or had single antigen vaccines in the past, to contact their GP practice in order to complete their immunisations with two doses of the MMR vaccine.'