According to The News International, the train on Monday morning carried 138 passengers who face custom and immigration clearance at Wagah border.
The Indian authorities said the operation of the train service was delayed on Sunday due to "track disruption because of labour issues".
However, the Pakistani authorities cited the reason as security issues due to protests in Amritsar.
The Indian Railways conveyed to Pakistani side that the service would not be operated on Monday as per its regular schedule, said The News International report.
Pakistani authorities were reportedly told that the Indian Railways allowed the operation as it was convinced the situation was under control and the train would not be sabotaged.
The Samjhauta Express is a twice-weekly train that runs on Tuesdays and Fridays.
