Chinese state media and the public have criticised the government and police for failing to prevent a New Year's Eve stampede in Shanghai that killed 36 people and dented the image of the city, China's financial hub.

The official Xinhua news agency said the government could not shake responsibility for what happened. It asked why there were apparently so few police on duty for the tens of thousands thronging Shanghai's famous waterfront, known as the Bund.

"It was a lack of vigilance from the government, a sloppiness," the news agency wrote.

Xinhua noted that the crush happened not far from a heavily publicised new free trade zone described as the "pride of the country".

The site of the stampede was cordoned off on Friday, with grieving relatives holding a candlelight memorial. Most victims were students in their 20s.

The waterfront has become a New Year countdown site in recent years after authorities brought in performances such as 3D light shows and fireworks. Celebrations in 2013 drew more than 300,000 revellers, and for the end of 2014, the government cancelled the show.

President Xi Jinping has demanded an investigation into the deadly stampede. He also urged local officials around China to ensure that no repeat of the incident could occur elsewhere during the upcoming Lunar New Year festival.

Police have dismissed reports that a rush to pick up coupons thrown from a bar overlooking the Bund was the cause, with focus shifting to overcrowding on a raised viewing area.

Source: Al Jazeera and agencies