Relatives of the 36 people killed in a New Year's Eve crush in Shanghai -- who are now closely supervised by the government -- have made a formal written demand for a proper account of the disaster, AFP has learned.

New Year revellers, many of them young women, were trampled after flocking to celebrations on Shanghai's historic waterfront known as the Bund, with severe overcrowding raising questions over why authorities failed to enforce stronger safety measures.

A petition drawn up by the family of one of the victims and seen by AFP blames Shanghai government officials, police and medical personnel for the accident and emergency response.

By doing so in writing it escalates the dispute.

"Lack of a plan, poor exchange of information, an inadequate estimate for security work are the direct causes leading to the entire incident," states the document, which has been circulated among victims' relatives.

It urged the Shanghai government to "satisfy requests of family members for the handling of funerals and relevant requirements for compensation".

Popular anger at authorities has increased after Caixin magazine reported that officials of Huangpu district, where the crush took place, had dinner at "high-class" Japanese restaurant near the site of the stampede on the night it took place.

"On one side, some were enjoying a gluttonous feast. On the other side, some were experiencing the final moment of their lives," said a microblog posting under the name Xiaoyu'er Aishang Yangguang.

Shanghai's Communist party corruption watchdog is investigating the dinner, which took place against the backdrop of a government austerity campaign, the official Xinhua news agency said Wednesday.

Attempts by AFP to reach the original drafter of the petition, the family of victim Gu Yinli, were unsuccessful. Gu, a 25-year-old white collar worker, had gone to the Bund with four friends, the Beijing News reported.

"Gu Yinli was in the first group of injured sent (to the hospital), she should have had a great chance of survival. A lack of timely treatment led to the loss of her life," the letter said.

- 'Extremely bad' impact -

Petitioning is a time-honoured method of seeking redress for grievances in China, from imperial times to the present. Under Communist Party rule, it is often the channel used when other avenues fail.

Other families confirmed they had received the document. Relatives said they were now completely "isolated", housed in designated hotels and followed by government minders when they go out.

The undated petition also alleged that the death toll was higher than the official tally. That claim could not be verified.

Shanghai Communist Party Secretary Han Zheng, the city's highest leader, has pledged an investigation into the crush.

Chinese media have reported that the central government's State Council, or cabinet, which usually handles major accident investigations, will not do so in this case, apparently leaving the inquiry in the hands of the local government accused of being responsible.

Some of the controversy has focused on the relocation of a light show on the Bund, with many revellers not properly informed or still going to the Bund, a large public space where people traditionally gather.

Chinese Vice Premier Ma Kai told a government safety meeting that the accident had an "extremely bad" social impact, in the strongest official condemnation of the accident.

Speaking on January 7, Huangpu party chief Zhou Wei said he and other district officials should "bear the responsibility" for the accident, Shanghai television reported, in the first such admission.

But observers say the question is whether higher level officials will share the blame.

Under China's rules for workplace accidents, those with death tolls above 30 are classified as "extremely large", and punishments for officials responsible include suspension, resignation or removal.