Bishop Oscar Cantu of Las Cruces has asked pastors, deacons and parish leaders in the diocese "to exercise increased vigilance in our parish surroundings and activities."
The bishop's message, posted early Aug. 4 on the diocese's Facebook page, was prompted by a small explosion that occurred Aug. 2 outside Holy Cross Catholic Church during the 8 a.m. Mass.
Earlier that morning, by about 20 minutes, a small explosion took place a few miles away at Calvary Baptist Church.
Minor damage was reported at both churches, but there were no injuries or deaths.
Federal and state authorities were investigating what explosives were used and trying to identify who was responsible for the blasts and whether they were connected.
At Holy Cross, the explosion occurred during the eucharistic prayer, according to Bishop Cantu.
Msgr. John Anderson, the pastor, told the Las Cruces Sun-News newspaper: "I was right in the middle of saying the words 'take and eat, this is my body,' and there was a pow! I mean, I knew it had to be more than a gunshot."
The priest said he "just kept on saying the words."
Several minutes later, police arrived on the scene and ordered the church evacuated, according to Bishop Cantu.
Msgr. Anderson went to the other side of the street with his parishioners, he said, and "there offered prayers for peace and safety."
Bishop Cantu said that over the next 24 hours, law enforcement authorities searched the premises for other explosive devices and to gather evidence.
"I was impressed with their thoroughness and professionalism," the bishop said. "It will surely take some time for the authorities eventually to find the perpetrator(s) and discover the motives of these criminal and violent acts."
Bishop Cantu said the diocese extended "prayers for and solidarity with" the Baptist congregation.
The AP reported that the explosive device at Calvary Baptist Church had been placed in a mailbox near the entrance to the church's offices. Police said several congregants were inside the church at the time, but services had not yet started.
"They will remain in our prayers," he said, adding that Msgr. Anderson and his parishioners also remained "in our thoughts and prayers, as they recover from the trauma of having their most sacred moments violently disrupted. ... We pray that, though with increased vigilance, the parish community will return to its routines of worship, formation, service, and community building."
Bishop Cantu urged parish communities to be aware of "any suspicious activity and report it to proper authorities. Let us do this with heightened awareness, but without alarm."
He added: "It is important that as much as possible we all return to our routines of parish, school, and community activities -- yet with prudent caution and awareness.
The bishop said that he and pastors held an Aug. 3 meeting and realized there is a need for emergency preparedness training in the parishes.
"We will certainly do so in order that our parish and Catholic school leaders can be prepared to respond to any emergencies that may arise," he explained.
"Let us pray for each other. Let us pray for peace," he said in closing. "Let us pray for the perpetrator(s), that they might discover the joy of peace and forgiveness and leave behind the frustration of hatred and violence.
"We pray for our first responders and those who work to maintain the peace. We pray for strength and healing."