Possible charges include desecration of a venerated object, criminal trespass, defacing property and bias-motivated crime, according to The Chieftan.
Although the incidents occurred in 2006, they only came to the attention of the parish when they were seen on the Internet site "Photobucket."
Robert Fotheringham, in charge of the LDS church's missionary program in parts of four states, and whose region includes the San Luis Valley, declined to release names of the missionaries. He confirmed the three missionaries seen in the photos, which have been removed from the Internet, were Mormon missionaries. He said they would be disciplined, though he declined to go into detail.
"We're just mortified this has happened. This is not what we're about," he said.
The Internet photos showed the three vandalizing the Shrine of the Mexican Martyrs in 2006 and mocking the Roman Catholic faith.
One missionary was seen holding the severed head of a statue. The head was found and restored.
Another photo showed a missionary appearing to preach from the Book of Mormon inside the Chapel of All Saints. A third photo showed one missionary pretending to sacrifice another on the altar at the Shrine of the Mexican Martyrs.
Members of the parish built the Shrine of the Mexican Martyrs, which has become a tourist attraction. No damage estimate was available.
"What they did was extremely imprudent, extremely uncharitable and inflammatory," the Rev. Pat Valdez told parishioners at a meeting Friday night. "You have worked hard and this whole community has worked hard to build that shrine as an expression of our faith and an expression of our love of God."
Fotheringham, meanwhile, met with parishioners to deliver a written apology from one of the three missionaries, signed by an R. Thompson.
"I realize that my companions and I have made a mockery of that which is most sacred to many of the residents of San Luis and the rest of the world. I should have known better because I have seen many of the same types of blasphemies made against my own church and I have been appalled," the statement said.
In a separate statement, LDS church authorities wrote that "those who were involved in this incident" face church discipline.
LDS church spokesman Scott Trotter said he did not know details about the discipline, whether the three still are serving missions or whether they still are members of the LDS church. Trotter said he also did not know when LDS church leaders first became aware of the pictures or whether the accusations will affect the missionary program.
When asked whether he was aware of any other acts of vandalism by missionaries against religious property, Trotter said, "I'm going to have to decline comment."
LDS church officials wrote in a statement Sunday that they were "deeply saddened" by the reported vandalism.
"It is particularly disturbing that this property was a religious site where people go to worship and find solace," the statement read. "We hope that the actions of these three will not damage our relationships with the citizens of San Luis and with the Catholic Church - relationships that we value so much. We offer our sincere apologies to all who have been affected by this senseless act.
"Those who were involved in this incident are facing Church discipline," the statement said.
-- Salt Lake Tribune reporter Erin Alberty contributed to this article.