The Rev. Barry Meehan resigned Sunday, though he denied "any improper activity," Bishop Thomas J. Tobin told parishioners at St. Timothy Catholic Church in Warwick during weekend services.
State police are investigating the matter and will interview the two suspected victims this week, The Providence Journal reported Monday.
"This is a very difficult time for the victim of this alleged abuse and his family, for Father Meehan and his family and friends, and for you, the people of St. Timothy's parish," Auxiliary Bishop Robert C. Evans said at mass Saturday and Sunday.
Meehan was the priest assigned to St. Timothy from 1978 to 2002. He has served at four other Rhode Island parishes. Police haven't said which churches were home to the alleged sexual abuse.
Some parishioners wept openly during the service, the newspaper said.