Baldacchino said the crisis created by the pandemic had brought about "a time for renewal."
"In the events of these days and weeks the Lord is calling us out of our comfort zone, he is calling us to seek new ways to reach the people. In addition to this mission with which we are entrusted, we also have the mission to keep people safe. The two must be equally pursued," he said.
"While it is true that we need to take every reasonable precaution to reduce the spread of Coronavirus, it is equally true that we offer the greatest 'essential service' to our people. The past few weeks have brought to light many unintended consequences of the 'stay-at-home' order."
The bishop pointed to reports that the Disaster Distress Helpline, a federal crisis hotline run by the Substance Abuse and Mental Health Services Administration, has seen an 891% increase of calls during the pandemic, with large spikes also being recorded at suicide prevention hotlines. He also noted reports of increases in domestic violence in places under lockdown.
"Simply put, in the midst of financial uncertainty, fear for one's health, pandemic induced anxiety and confinement to their homes, people definitely need a word of hope," he said.
"We, as priests, are called to bring the Word of Life to people, we are called to minister the life-giving sacraments. Televised Masses have been an attempt to bridge the gap during this time, but I am increasingly convinced that this is not enough," Baldacchino said.
"The eternal life offered in Christ Jesus needs to be announced. It was precisely the urgency of this announcement that drove the first apostles and the need is no less today. Christ is alive and we are his ambassadors."
Revoking the suspension of public Masses, in place in the diocese since March 16, the bishop said that priests are now allowed to celebrate Masses in the presence of the faithful "while maintaining all current health precautions set forth by the state and federal government."
Baldacchino's letter noted that the state of New Mexico recently updated its Public Health Order, which no longer includes churches as "essential services."
"I strongly disagree," he said. "Sadly, the Governor is no longer exempting places of worship from the restrictions on 'mass gatherings.' It seems to me that while we run a daily count of the physical deaths we are overlooking those who are dead interiorly."
To comply with the governor's directive, guidelines issued to all priests limit attendance at Mass in church buildings to 5 people, including the celebrant, and insist that a minimum safe distance of six feet be observed and all seating sanitized after Mass ends.
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Baldacchino also authorized priests to celebrate Mass outdoors, in compliance with state guidance on social distancing, and specifically recommended setting up an altar in the parish parking lot with parishioners remaining in their cars with an empty space between each vehicle.
"Parishes that lack sufficient parking spaces may celebrate the liturgies in open cemeteries or other available open spaces. Parishioners should maintain at least a six feet separation at all times," the guidance states.
Over the Easter Triduum, the bishop had a stage erected outside the Cathedral of the Immaculate Heart of Mary and celebrated the liturgies of Holy Thursday, Good Friday and the Easter Vigil for local Catholics who remained in their cars.
The guidelines also lay out strict instructions for the distribution of Communion, with priests told to wear a face mask, sanitize their hands, and wear gloves for the distribution.
Baldacchino also encouraged priests to continue hearing confessions and ensure that the anointing of the sick was still available where necessary.
"Priests may and should continue to offer" the sacraments, he said. "The faithful are not to be deprived of this sacrament, especially when in danger of death."