The tragedy struck minutes before midnight yesterday when people rushed to see a live show at a small crowded place in the city's popular riverfront Bund area, police said.
The latest mishap at about 11:35 PM local time (21:05 IST) came as the cosmopolitan city's worst disaster since 58 people died in an apartment building fire in 2010.
Witnesses said a large number of people rushed upstairs while those already there began moving down through narrow steps. An injured person said as a result, those moving up fell down, causing a huge pile of people that led to heavy casualties. Those who fell were trampled on by others in panic.
Witness Wu Tao said some coupons were being thrown from a building's third-floor window near the Bund and people standing along the river bank started to scramble for those coupons.
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The stampede was a "wake-up call that the world's second- largest economy is still a developing country which has fragile social management", it said in an unusually critical commentary.
Among the 36 dead was a Taiwanese and 25 of the killed were women, the report said, adding that the ages of the first 10 identified fatalities ranged from 16 to 36. (MORE) PTI KJV GVS ASK SAI AKJ
Some people on social networking websites said they found pictures of the bar owner showing off those coupons before the incident. But the blogger, who called herself "Chaojidadadashabao_MissShen" on the Sina Weibo, denied she threw away any coupons.
Chinese President Xi Jinping ordered an immediate investigation into the incident and called for proper treatment of the injured. Such incidents during celebrations should be prevented, he said in a message.
Li called for making "every effort" to reduce injury- related deaths and consoling relatives of the victims of the stampede.
The Bund, famous for its colonial architecture, is the former financial district of China's commercial hub and now a popular tourist destination.
Shanghai residents have traditionally flocked there to celebrate New Year, and more recently the district government overseeing the area has staged official celebrations.
This year's "countdown" was scaled down and moved to a new location away from the main Bund specifically due to concerns about overcrowding after nearly 300,000 people turned up to witness the spectacle last New Year's Eve, the Shanghai Daily newspaper reported.