Official sources said some of the students were charred to death while some jumped off the four-storey building in panic and died as they fell.
Fire Brigade sources confirmed that 17 students were killed in the incident at the Takshashila Arcade building in Sarthana area. Officials feared that the death toll could go up further.
The coaching centre was being run on the covered roof-top, which effectively became the fourth storey, and there was a wooden staircase to reach there, witnesses said.
The authorities of the Surat Municipal Corporation were inquiring whether the building had taken the statutory permission, including regarding fire safety.
Gujarat Chief Minister Vijay Rupani, who ordered an investigation into the incident by Mukesh Puri, Principal Secretary, Urban Development, himself rushed to Surat.
He also announced a financial help of Rs 4 lakh each to the families of the students who died.
Shocked by the incident, Prime Minister Narendra Modi posted on his tweeter handle: "Extremely anguished by the fire tragedy. My thoughts are with bereaved families. May the injured recover quickly. Have asked the Gujarat government and local authorities to provide all possible assistance to those affected."
Several other leaders, including Congress President Rahul Gandhi, also condoled the death of the students.
( With inputs from IANS )