One of the 36 funerals for the victims of a New Year's Eve crush in Shanghai was held Tuesday, after authorities finally allowed the ceremonies to go ahead.

Du Shuanghua, 37, lay in an open coffin at a funeral home in the city centre as friends and relatives placed flowers on both sides.

"I'm taking him back to his hometown tomorrow to let him rest in peace," his wife Fan Ping told AFP. They had an eight-year-old son and Du was the family's only breadwinner.

New Year revellers flocked to the Bund, Shanghai's historic waterfront, but massive overcrowding saw people trampled, severely tarnishing the commercial hub's image as the mainland's most advanced city.

Questions were raised over authorities' failure to enforce better safety measures and several district officials were dismissed from their posts, although higher-level leaders escaped responsibility.

In the meantime the families of the victims were "isolated", they said, and funerals were blocked until an official accident report was released and compensation agreed.

The document was published two weeks ago, along with an offer of 800,000 yuan ($131,000) for each family.

Those who accept the package are being allowed to lay their loved ones to rest, with some ceremonies taking place this week.

Cai Jinjin on Monday attended the funeral of her cousin Qi Xiaoyan, who like most of the victims was a young woman.

Qi, a 21-year-old migrant, had come to Shanghai from nearby Anhui province just months ago for work.

"Dear sister, have a safe trip. I'm sending you home... we will take care of the rest for you," Cai said in an online posting.

Speaking at his first press conference after the incident, Shanghai Mayor Yang Xiong said the city would improve safety measures in public spaces.

"After the 12.31 (December 31) incident, we have been asking ourselves how to do our work better," he told reporters on Thursday. "We have to learn the lesson the 12.31 accident taught us."