Sarveshwar Sharan, 40, allegedly repeatedly acted in a way that caused "fear and alarm" while in a position of trust as priest.
He faces two charges of making inappropriate sexual remarks to two women and attempting to cuddle them.
The alleged incidents are said to have taken place between October 2012 and July 2013, at La Belle Street, Glasgow, and between April and July 2013 at a Hilton hotel gym and at Paisley Road West.
Sharan is also accused of entering a female's bedroom uninvited.
He appeared at Glasgow Sheriff Court where he pled not guilty to the charges.
Trial was set for next month.