Witnesses told the South China Morning Post that the tragedy could have been prevented if police had managed the crowd as it had in the past.

“The tragedy could have been avoided if enough police officers had been dispatched to maintain order,” Ma Xiaobang, a witness in his early sixties, said. “I have been there every year to join in the fun but there had never been such chaos as this.”

The cause of the crush remained under investigation, Xinhua said.

New Year celebrations across Shanghai were cancelled today after the incident.

Forty-nine people were injured amid the chaos in the city's popular riverfront tourist district about half an hour before midnight, according to a statement released by the city government. Thirteen are in a critical condition, the authorities said on the government's social media account. 

Most of those killed and injured in the stampede were young people in their 20s, including college students, the official Xinhua news agency said. 

Shanghai authorities have identified 33 of the injured, including two Taiwanese and one Malaysian, and one Taiwanese was confirmed to be among the dead, according to the twitter account of state broadcaster CCTV News.

Watch: New Year stampede kills 36 in Shanghai

The authorities in Shanghai cancelled all New Year celebrations on Thursday as President Xi Jinping instructed them to "do everything in their power" to help those injured and launch an immediate investigation into the cause of the stampede, according to state media.

Local media quoted survivors and witnesses describing the chaotic scene as waves of spectators in a square swarmed onto a raised platform for a viewing spot of a New Year's Eve light show and pushed against those coming off, with people pressed so tightly together that they couldn't breathe.

As exhausted people fell or were knocked down, tripping more behind them, panic quickly spread through the huge crowds, with "young girls screaming desperately for their lives and the sounds of all sorts of curses around", wrote one eyewitness on social media.

Survivors described the scene as "hellish", Xinhua reported. 

One man caught in the crush was quoted on a social media account of a 21st Century Business Herald journalist as saying that the chaos lasted for about 10 minutes.

"I was surrounded by cries for help from women and the sounds of beating and cursing," he said. "All I could do was try to keep my upper body in the air to ensure that I could breathe.

"There were people behind me grabbing my hair, struggling for breath, and a girl held me saying, 'Help me, I can't hold on much longer'". There were also women who had fallen silent beneath me."

When the crowds finally thinned, dozens of victims were seen lying unconscious or moaning on the ground and on top of each other. Volunteers and survivors helped carry some victims to open areas and tried to resuscitate them as others started calling the police and emergency services.

"That was when we heard the count down: 5, 4, 3..." wrote one witness on Weibo. 

"There were just too many people and nowhere people could escape to," said a woman witness who declined to give her name.

Cui Tingting, 27, said she had picked up some of the coupons, but had thrown them away when she realised they were not money.

"It’s too cruel. People in front of us had already fallen to the floor and others were stepping all over them," she said.

Cai Lixin, a police commander in the district, told a press conference that 500 officers were deployed at the scene to help with the rescue operation and disperse the crowds.

Some of the injured were sent to hospital by police car before ambulances arrived, he said.

A Xinhua photo from the scene showed at least one person doing chest compressions on a shirtless man while several other people lay on the ground nearby, amid debris. 

At Shanghai No1 People’s Hospital, waves of anxious people were rushing to the emergency ward on Thursday morning, looking for their loved ones after learning of the midnight stampede in the news. Some said they had lost contact with their children or friends and were worried that they might be among the casualties.

They were barred from entering the ward by policemen and hospital security guards, while police circulated pictures and name lists of injured victims who had been sent to several city hospitals, asking family members to identify them. 

A brief scuffle broke out as one middle-aged man lost his patience and tried to push through the line of security guards. The Shanghai resident told the South China Morning Post that he had waited for hours for news about his 25-year-old nephew, who was being treated at the hospital.

“It is such a serious incident and why is there no government official or hospital staff here to speak to us? They left all this to a few young security guards to handle?” he said after arguing fruitlessly with the security guards.

Four university students from Jiangxi Province told the Post that two of their female schoolmates were among those hospitalised. The square where the stampede took place was extremely crowded, they said. It was difficult to move around, and mobile networks were jammed. 

The four were separated from their schoolmates and left the square amid the chaos after the countdown. They only learned that the other two girls were injured and hospitalised from news reports, they said.  

At the same hospital, the mother of an injured 12-year-old boy sat crying, surrounded by relatives. 

“We don’t know what is happening, but we can’t get in to see him,” said her older brother, who declined to be named.

One of the people killed was from Taiwan, Xinhua reported. Another person from the island was also injured, the news agency said.  

A person from Malaysia was also hurt in the crush, the People's Daily reported.

One local woman killed was a student Du Yijun, who was studying at Fudan University in Shanghai, the Shidao Bao newspaper reported. She was pronounced dead at hospital. 

Premier Li Keqiang told the Shanghai authorities to "take all possible measures to reduce the number of casualties", Xinhua reported. Shanghai Communist Party secretary Han Zheng and mayor Yang Xiong went to several local hospitals to visit victims after the stampede. 

The city should immediately examine its schedules of large events, especially events in densely populated areas, the official China News Agency quoted Han as saying. "All those that should be stopped must be stopped," 

Hong Kong's Immigration Department had not received any request for assistance from Hong Kong residents so far in relation to the Shanghai stampede, a government spokesman said on Thursday. 

Last week, the English-language Shanghai Daily reported that the annual New Year's Eve countdown on the Bund that normally attracts about 300,000 people had been cancelled, apparently because of crowd control issues.

The report said a "toned-down" version of the event would be held instead. Many of the huge crowds had come to see a light show that started at 11pm and was due to end after midnight. 

The stampede appeared to be near that area.

Witnesses said there were a "sea of faces" and they struggled for breath amid the crowds. 

Shanghai's historic Bund riverfront runs along an area of narrow streets amid restored old buildings, shops and tourist attractions. The China Daily newspaper in February reported that the city's population was more than 24 million at the end of 2013.

Last year, 14 people - some of them children - were killed and 10 injured in a stampede that broke out as food was distributed at a mosque in China’s Ningxia region.

Also last year, six students were killed in a stampede at a primary school in Kunming in the southwest, after the accidental blocking of a stairway corridor.