The proposed bill would ban under 18s from using sunbeds and ensure sunbed use by adults was supervised
A law banning under-18s from using sunbeds is possible before the general election, says the MP proposing it.
Cardiff North MP Julie Morgan has put down a Private Member's Bill calling for the ban, and all other sunbed use in Wales and England to be supervised.
She said: "There's a huge amount of support for it - we just need bit of luck and goodwill."
Public Health Minister Gillian Merron said the UK government "fully supports" Ms Morgan's proposals.
British Medical Association Cymru said the proposed law would "close a loophole" in protecting the public.
Ms Morgan's bill comes after a study last month found some 250,000 11-to-17-year-olds in England were risking skin cancer by using sunbeds.
The research, the first looking at use by under-18s, reported that a quarter of under-18s who used sunbeds did so at least once a month.
Cancer Research UK called for a ban in England on their use by under-18s.
A new law preventing under-18s from using sunbeds came into force throughout Scotland this month.
In September, a Welsh Assembly Government assembly government survey showed there were 419 tanning outlets in Wales of which 46 were unstaffed salons.
Last week, a tanning salon owner was sentenced to community service at Barry Magistrates' Court, Vale of Glamorgan, after he admitted five health and safety offences.
The bill comes after a 14-year-old girl burned after using a tanning machine
He was investigated after a 14-year-old girl received 70% burns in his unstaffed Lextan salon in Barry in February.
Ms Morgan said she was aware of this case and the campaigning about the issue of unregulated sunbed use.
She said she plumped for a second reading of her bill on 29 January so it would have more time at the committee stage.
She said: "Because the general election is bound to be in May, I wanted to go for something that has a real chance of becoming law.
"It's really now a matter of timing and trying to get it through. There's a huge amount of support for it. It's something that we can do that's very practical that would protect the public.
"I have solid evidence that harm is being done, there appears to be no doubt about that, there's not likely to be any argument.
"I'm sure most people are responsible [in their sunbed use] but we know that it happens."
She said many young people thought it was a "wonderful thing" to have a tan.
She added: "People have this image of themselves and a tan. I can understand why - people who are tanned do look healthy but in the long term it is damaging.
"For too long children have not been protected from using sunbeds. This bill would not only ensure that children are protected but that adults who do use sunbed salons would have access to accurate health information."
Richard Lewis, Welsh secretary of the BMA, said: "There is no such thing as a safe tan (unless it comes out of a bottle).
"It's ironic, people use sunbeds because they think they'll look better and yet they will probably end up looking old prematurely and possibly getting skin cancer."
Skin cancer rates are rising faster than any other type of cancer and have more than quadrupled in the last 30 years - rising from 3.4 people per 100,000 in 1977 to 14.7 per 100,000 in 2006.
Ms Merron said: "Cancer Research UK's recent report, commissioned by the government, showed worrying levels of sunbed use by under 18s and confirmed that voluntary action by the industry is not enough to protect young people."