It is the race within the race: while rescuers inch towards the trapped miners rival churches tussle over the miracle in the making. Evangelical, Adventist and Catholic clerics are vying to stamp their own particular faith on a surge in religious fervour as the drama nears a climax in Chile's Atacama desert.

The three Christian denominations have each claimed credit for what they say is divine intervention in the survival – and expected imminent rescue – of the 33 men who have spent 67 days beneath the earth.

"God has spoken to me clearly and guided my hand each step of the rescue," said Carlos Parra Diaz, a Seventh-day Adventist pastor at the San Jose mine. "He wanted the miners to be rescued and I am His instrument."

Yards from where he spoke Caspar Quintana, the Catholic bishop of Copiapo, prepared an altar to celebrate an outdoor mass for a small congregation of miners' relatives and phalanx of TV cameras. "God has heard our prayers," said the bishop. "I have received comments of encouragement from all over the world. Let us give thanks."

A litte bit further up the hill of Camp Hope, the improvised settlement of miners' families, rescuers, government officials and media, an evengelical preacher, Javier Soto , wandered from family to family with a guitar and songs of praise. "He listens to the music," said the pastor, gesturing to the azure sky.

Each church has reported a spike in religious faith in Chile and beyond, with candle-lit vigils and online communities following each step of preparations to extract the miners one by one in a capsule dubbed the phoenix.

Diaz, an intense 42-year-old dressed in black, claimed to be the first cleric at the mine and said it was no coincidence an exploration probe reached the trapped men - 17 days after the August 5 collapse - while he was praying above.

"The first probe missed them, they heard it going in the wrong direction, and thought they were doomed, that they'd starve to death. But the second probe went right to them."

Diaz mobilised colleagues in the capital Santiago to find miniature, 7cm-wide bibles to fit into the "pigeon" tubes which delivered supplies to the men below. He sent one to each miner, earning a letter of thanks from Jose Ojeda, the master driller.

None of the miners are Adventists but six have relatives who belong to the church, which believes in the imminent second coming of Christ.

Diaz stole a march over his rivals by obtaining permission to give a 10-minute talk to the assembled 33 families before their nightly briefing by government officials. "I do macro work. I am pastor to all." The other churches, he said, did "micro" work.

The pastor claimed his Catholic rival had trekked up to the bleak, muddy site just three or four times. Bishop Quintana, after concluding a mass in which TV cameras outnumbered worshippers, declined to be drawn on the subject of competition but said he had received supportive emails from all over the world. "What matters is that God is acting through human ingenuity to rescue these men."

Shrines to the men dotted around the site are adorned with statues of saints and posters of religous figures such as Pope John Paul II.

Some members of "los 33" who were not religious before, such as Franklin Lobos, have found faith during their ordeal, said family members. When the mine collapsed dust filled the chamber, blotting out lights, but what appeared to be a "white butterfly" led him to the refuge and safety, said his brother, Manuel Lobos.

"Imagine, a little white thing flitting through all that, leading him to the others. It was a miracle," said Manuel, 67. "A pastor told us that that this was an angel."