Two observers from the Guinness Book of World Record were present.
Delegates will also visit the Ardh Kumbh Mela and the Republic Day Parade in Delhi.
President Kovind and first lady Savita Kovind offered prayers at the Sangam.
The congregation began with the ‘Shahi Snan’ on Makar Sankranti.
The trains will wear the Kumbh 2019 logo on its coaches.
The first passenger train in India ran between Mumbai and Thane on 16 April 1853.
The state is known for the Kumbh Mela and other popular tourism and pilgrimage centres.