The priest has admitted committing some sex acts with children between the ages of 9 and 14, two of whom had disabilities, said investigating magistrate Yvonne Gendre.
However, the 68-year-old priest, who was not named because of privacy laws, has denied accusations that he molested two children who subsequently committed suicide, Gendre told reporters in the western city of Fribourg.
The priest also denied accusations by some of the victims that he sodomized them, she added.
Swiss officials began investigating the priest after being informed of accusations against him by their French counterparts.
The legal time limit for prosecution has expired in all but one case, which occurred in the French city of Grenoble in 1995.
Gendre said she will hand the investigation over to justice officials in Grenoble who will decide whether to press charges against the priest.
Gendre expressed horror that the man was able to carry out the alleged abuses for more than three decades.
She said the priest, who belongs to the Capuchin order, an offshoot of the Franciscans, was transferred or dismissed from his post three times because of allegations against him, but continued to work for the church.
The Catholic Church has been plagued by a series of sex abuse cases against clergy that have come to light since 2002 and spread throughout the United States and beyond.
A spokesman for the diocese of Fribourg acknowledged that the case raised some questions.
"Obviously we are concerned," Marc Donze told The Associated Press. "But suspicion isn't the same as proof."
Gendre said another priest is under investigation for similar crimes.
Procedures have since been put in place to speed up the church's investigation of such allegations.
According to the Swiss Society for the Protection of Children, 364 people in Switzerland were convicted of sexually abusing children in 2006, the last year for which official figures are available.
The group describes the figures as "the tip of the iceberg."
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(Source: AP)