Singh said the chief minister was very sad after the shocking incident.
State Home Secretary Amir Subhani has began an inquiry into the stampede.
"We have began an inquiry into the cause of the stampede," Subhani told mediapersons in Patna.
Nitish Kumar at a press conference Monday night (11 p.m.) here refuted reports that a bamboo bridge collapse caused the deaths and said it was due to a stampede.
According to an official in the chief minister office, Nitish Kumar has directed the top health department officials to provide treatment to the injured.
Opposition Rashtriya Janata Dal chief Lalu Prasad is likely to arrive in Patna from Delhi to meet the families of those killed and visit injured in the hospitals.
At least 18 people, including children and women, were killed and many others were injured in a stampede during the Chhath puja and celebrations in Patna Monday evening.
Celebrated six days after Diwali, Chhath is dedicated to the Sun god. During the festival, married women observe fast for 36 hours, and devotees offer wheat, milk, sugarcane, bananas and coconuts to the Sun god.