The children were aged between four and seven and lived in the city of Weihai in Shandong province where the accident happened.
The children were aged between four and seven and lived in the city of Weihai in Shandong province where the accident happened, a South Korean consular official in the city of Qingdao told AFP.
The Weihai propaganda department said on a microblogging website that 12 people had died and another person was seriously injured.
Officials did not immediately give the nationality of the two others killed and the injured person.
South Korea's Yonhap news agency, citing its embassy in Beijing, said the two other fatalities were a Chinese child and the driver, while the injured person was a teacher.
The bus burst into flames in the tunnel at around 9:00 am, according to Xinhua news agency. The cause of the crash was under investigation.
An amateur video posted by the People's Daily on its Twitter account shows cars driving away from the bus, which was stopped near a wall as flames reached the tunnel's ceiling. The video's authenticity could not be immediately verified.
The students attended a kindergarten affiliated with an international school that largely caters to South Koreans, according to Yonhap.
South Korea's Acting President Hwang Kyo-Ahn voiced "grave sadness" over the tragedy, which occurred as the country went to the polls to elect a news president.
Hwang told the foreign ministry to mobilise "all diplomatic resources" to handle the accident and keep the parents of the young victims informed of any developments.
Deadly road accidents are common in China, where traffic regulations are often flouted or go unenforced by police.
There were more than 180,000 traffic accidents and 58,000 deaths in 2015, authorities said in December.
The country's frequently overcrowded long-distance buses are particularly prone to high fatalities.
Ten people were killed and 38 injured in March when a bus collided with a cement truck in the southwestern province of Yunnan.
At least 18 people were killed when a minibus plunged into a lake in the central city of Wuhan in December.
Last November, a pile-up on an expressway in the northern province of Shanxi killed 17 people and damaged 56 vehicles.