“All Christians know that God can appear at any time,” said Antonio Socci, a journalist and author who covers the Roman Catholic Church. But he added, “experiencing a supernatural event that’s ongoing and in the here and the now” is what has lured so many.

“Medjugorje is a huge mass phenomenon,” Mr. Socci said.

Even so, the reported apparitions have also fueled controversy, in large part because of their duration, and clockwork regularity. Though the church has recognized many dozens of apparitions of the Virgin Mary in the course of its history, rarely have such claims lasted as long.

The longest apparitions are those said to have occurred in Laus, France, from 1664 to 1718, when Mary appeared to the Dominican sister Benedicta Rencurel. The church did not approve them until 2008, 290 years after Sister Benedicta’s death.

The six youths who first reported seeing Mary, in 1981, when they ranged in age from 10 to 17, are known as the visionaries. Three of the six say that since then, they have had only periodic visits. Skeptics raise eyebrows not least because, at times, the visionaries have promised apparitions during public appearances in advance.

Doubters accuse the visionaries of blurring the line between the spiritual and the material by capitalizing on the apparitions through global speaking tours and investments in the local tourism industry.

“You have to bear in mind that the visionaries have built economic interests here,” said one skeptic, Marco Corvaglia, a high school teacher who chronicled what he claims are the visionaries’ conflicts of interest on his blog.