Dr Andrew Dearden. of the BMA, said parents needed to make a choice based on "fact not fear".
An assembly member wants a debate on introducing an element of compulsion over vaccinating children with the MMR triple vaccine.
Torfaen AM Lynn Neagle believes Wales should follow the example of the US, where children who are not vaccinated cannot start state school.
The current outbreak of measles, which the MMR jab protects against, has caused 253 cases of the disease.
More than 30 people have been treated in hospital across the country.
It is the largest outbreak of the disease since the MMR vaccine was introduced in Wales more than 20 years ago with 88 cases in the mid and west Wales area, 57 in north Wales and eight in south east Wales.
Meanwhile, Dr Andrew Dearden, who represents GPs at the British Medical Association, told BBC Wales that doctors were beginning to see more cases of mumps.
He added that MMR was safe and there needed to be a return to a position where parents made a choice "made on fact, not fear".
Ms Neagle, who has two children, aged six and 10 months, told BBC Wales she would be raising the issue in the Welsh assembly and health professionals.
"I think it's quite clear now that some major action does need to be taken," she said.
"We're in the middle of a serious measles outbreak. All public experts agree its only a matter of time before we see the first measles death in Wales for many years.
The illness is associated with a blotchy rash which spreads down from the face
"What we need now is a debate about how we bring MMR vaccines up to the level that would prevent that kind of thing happening.
"As you know we had a report [on the MMR] many years ago which has been thoroughly discredited and we have not seen the increase in immunisations which would prevent outbreaks such as the one we're in.
"I want a debate on whether it's time to move to an element of compulsion on the MMR."
Some have suggested the government should offer single vaccines for those parents who still do not want to have their children immunised with the MMR, which also protects against mumps and rubella.
However, Ms Neagle said it would be "irresponsible" to pursue a single vaccine campaign.
She said her eldest child had had the MMR but the other one was not yet old enough, which worried her.
"My other child is still a baby and is too young for the MMR, and it's those children who are most at risk from the measles outbreak and are being put at risk by the decision not to give children the MMR."
On Saturday, 47 children were taken from the Llanelli and Swansea areas to a private clinic in Worcestershire to have single measles jabs, despite official advice to receive the free NHS MMR vaccine.
The clinic they attended, Desumo, had 50 children signed up to receive vaccines in Llanelli on Saturday but could not get a licence to run the clinic in time.
The company said it was responding to public demand offering parents an alternative to the triple MMR vaccine - a single jab advertised on its website for £75.
Health chiefs in Wales have previously said the single vaccine is a "red herring" and are warning parents against using it.
Wales' Chief Medical Officer Dr Tony Jewell said he was concerned about their safety and effectiveness.
He said: "There is no need for parents to spend money on a vaccine when there is a proven, safe and effective alternative in the combined measles, mumps and rubella (MMR) vaccine that has been used across the world for more than 20 years."
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.