The injured man was taken to hospital and was now recovering in ICU after surgery, Leitch said.
Police wanted to hear from anyone with information which could help their inquiry.
"The male offender left the scene along York St after the incident and police are seeking the help of the public to identify him."
The man is described as being of medium build, about 175 centimetres tall, wearing a dark baseball cap and light-coloured hoodie.
A white Mitsubishi L300 van parked in the church carpark left shortly after the stabbing and it was believed the occupants may have witnessed the incident, Leitch said.
"We ask that they contact us."
Anyone with information should contact police on 105 or, anonymously, via Crimestoppers on 0800 555 111.