Emergency officials received at least 81 calls from people in Itaewon saying they were having difficulty breathing, Yonhap news agency reported.
The stampede took place near the Hamilton Hotel in the nightlife district of Itaewon, as a large number of people were believed to have entered a narrow alley near the hotel.
President Yoon Suk-yeol, who presided over an emergency meeting on the stampede, ordered officials to swiftly administer first aid and treat the injured, the presidential office said.
Yoon also ordered officials to deploy emergency medical officials to Itaewon and secure emergency beds.
Separately, Prime Minister Han Duck-soo instructed officials to make utmost efforts to minimise damages.
Meanwhile, Seoul Mayor Oh Se-hoon, who is on a visit to Europe, decided to return home in the wake of the accident, city officials said.
A total of 142 firefighting vehicles have been mobilised for the area.
Including some 50 people who suffered cardiac arrest, fire authorities estimated about 100 people were hurt.
As of around 1 a.m. Sunday (local time), a total of 21 people, mostly women in their 20s, had been sent to emergency rooms, officials said.
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