The stampede occurred at around 1.30 p.m. at the Rajghat bridge in the Ramnagar area, as thousands of people, who had turned up at a religious congregation organised by disciples of the late spiritual leader Jai Gurudev, took out a procession.
Ramanagar police station incharge Anil Kumar Singh told IANS that 19 people were killed in the stampede and over 60 injured.
Police attributed the stampede to the "impatience" among the participants due to the prevailing heat and humidity, and also noted that while the organisers had sought permission for presence of around 3,000 people, nearly 80,000 had turned up.
Varanasi's Senior Superintendent of Police, Akash Kulhari said: "The participants were feeling uncomfortable in the heat due to which the stampede might have occurred."
He said that as the incident spot was on the district boundary with Chandauli, police from both areas had reached the spot for rescue and relief operations.
An officer at the spot said that they were focussing on relief and rescue operations and "a probe will be ordered later to ascertain the exact cause of the tragedy".
Chandauli District Magistrate Kumar Prashant told IANS that an awareness camp for Baba Jai Gurudev's was going on in Domri village, on the banks of the Ganga, in the district, and a large number of devotees from Varanasi's Pili Kothi area were on their way there when the stampede occurred.
He said that the injured had been admitted to hospitals where the condition of five was said to be critical. The deceased have not been identified yet, he added.
Chief Minister Akhilesh Yadav has announced compensation of Rs 5 lakh each to kin of the deceased.
Varanasi is also the parliamentary constituency of Prime Minister Narendra Modi, who expressed his grief over the incident.
"Deeply saddened by the loss of lives in the stampede in Varanasi. Condolences to the bereaved families. Prayers with those injured," Modi tweeted.
"I have spoken to officials and asked them to ensure all possible help to those affected due to the stampede..," he said in another tweet.
Congress president Sonia Gandhi and Vice President Rahul Gandhi also expressed shock and grief over the deaths.
Hoping that the authorities concerned were providing adequate medical relief and compensation to the victims, she also instructed party workers to provide all possible assistance to the people, a Congress statement said.
Rahul Gandhi, in a statement, said: "Shocked and deeply saddened to learn of the stampede in Varanasi. My heartfelt condolences to families of the victims of this tragic incident."