Parents living near Japan's crippled Fukushima nuclear plant are facing a nightmare dilemma: evacuate their children or live with the fear that radiation will make them sick.

Since the crisis started on March 11, authorities have raised the exposure limit for children to that used for atomic plant workers in many countries but have sought to reassure families their children are safe.

Some people have listened to the official advice, then voted with their feet and moved out of the fallout zone, but most have stayed, reluctant to give up their jobs, homes and lives, despite the lingering fear.

In Fukushima city, home to 300,000 people, playgrounds are eerily quiet while children play indoors, one layer removed from the dangers of the atomic plant 60 kilometres (40 miles) away on the tsunami-ravaged coast.

Most schools have banned children from playing football or baseball on outdoor fields or splashing around in swimming pools exposed to the sky. The windows of classrooms remain shut despite a summer heat wave.

More than 300 children have left the city's elementary and junior high schools since April, says the education board in Fukushima, where town workers have been washing down the walls of school buildings.

"We fully understand the feelings of parents, but we want them to act calmly," board official Yoshimasa Kanno told the media, adding that the city will hand a radiation dosimetre to every student by September.

One mother, Sachiko Sato, 53, who lives in Kawamata, just 35 kilometres from the crippled plant, has moved her two children to another town, although she has stayed behind in the family home.

"We asked ourselves what's most important to us," she said. "For some people it's their job, for others its family ties. For me it's my children's future."

Another parent, Hiroshi Ueki, 40, a former kindergarten worker, moved his wife and two sons, aged one and four, to Matsumoto in the mountainous prefecture of Nagano, 280 kilometres away.

Remembering family life in their home town, he said, "everyday I used to tell my sons: 'Don't touch this. Don't eat that. Don't take your mask off'."

"When we got to Nagano, my son was still asking me: 'Dad, can I touch this flower? Can I touch that car? Can I play in the rain?' When I heard him say that, I was almost crying."

Ueki is one of a growing number of local citizens who, in a movement rarely seen in consensus-seeking Japan and fuelled over the past four months by social media, are challenging the government.

"The government is saying it's safe and secure," said Ueki, who is back in Fukushima, trying to convince other parents to leave.

"But they can really only say that 10 years, 20 years, 30 years from now, if nothing has actually happened by then."

Japan's radiation limit was raised from 1.0 to 20 millisieverts per year after Japan's worst quake on record triggered a tsunami that slammed into the Fukushima plant, triggering a series of meltdowns and explosions.

In Fukushima city, authorities now estimate aerial exposure of 5.4 to 13.6 millisieverts per year not counting, critics point out, any internal exposure from food or dust contaminated with radioactive isotopes.

Fears were fuelled when a recent test showed small amounts of radioactive substances in the urine samples of all of the 10 children surveyed.

According to the Fukushima Network for Saving Children from Radiation, which carried out the tests with a French non-government group, 1.3 becquerels of caesium-137 per litre was found in the urine of a seven-year-old boy.

Japan's central government downplayed the concern, with the education and science minister, Yoshiaki Takagi, stating that the level was too low to affect children's health immediately.

Many doctors have also advised parents in Fukushima not to overreact if their children suffer symptoms such as bleeding or diarrhoea, saying they are unlikely to be related to radiation under current exposure levels.

But they also argue that authorities should not reach hasty and easy conclusions, saying that the findings at least show that children in Fukushima have been exposed to a certain level of radioactivity.

Radiation safety experts agree that children face a higher risk from radiation-linked cancers and other diseases than adults, but they disagree on just how high the risk is, amid a global dearth of long-term studies.

"It has been medically proven that children can be at greater risk of radiation exposure than adults," said Tokyo paediatrician Makoto Yamada.

"No-one can accurately predict the eventual physical impact of radiation on people in Fukushima," Yamada told the media. "It is the authorities' duty to take careful measures considering the worst-case scenario."

One radiation expert, Toshiso Kosako of Tokyo University, quit his government advisory job in tears in April when the radiation limit was raised, saying he wouldn't expose his own children to those levels.

Another fearful Fukushima parent is medical worker Masayoshi Tezuka, 42, who evacuated his two daughters for a while, then brought them back, citing the stress of splitting the children from their working parents.

Tezuka said he was shocked when he recently saw pictures of Ukrainian children with neck scars from surgery for thyroid cancer, blamed on radiation exposure from the 1986 Chernobyl nuclear accident.

"In my mind I swapped their faces with those of my daughters," he said. "It was dreadful. I'm still wondering if this is what will one day happen to my daughters. That fear is still haunting me."