JERUSALEM — It was a typical day at the shrine around what many believe is the tomb of Jesus in Jerusalem’s Old City. A Greek Orthodox choir sang inside a room facing the baroque structure. But the voices were drowned out when chanting Armenian priests and monks circling the shrine raised theirs.

“Sometimes they punch each other,’’ Farah Atallah, a church guard wearing a fez, observed with a shrug.

Atallah is a seasoned witness to the rivalries among the Greek Orthodox, Armenian Orthodox, and Roman Catholic communities that jealously share — and sometimes spar over — what they consider Christianity’s holiest site, inside the Church of the Holy Sepulcher.

Amid the rivalry, the unsteady 206-year-old structure, held together by a 69-year-old iron cage that honors the keystone of Christianity, the tomb from which Christians believe Jesus was resurrected, is an uncomfortable, often embarrassing symbol of Christian divisions, which have periodically erupted into tensions. In 2008, monks and priests brawled near the shrine, throwing punches and pulling one another’s hair.

But in recent weeks, scaffolding has gone up a few feet from the shrine in the gloomy shadows of the Arches of the Virgin, the first step in a rare agreement by the various Christian communities to save the dilapidated shrine, also called the Aedicule, from falling down.

The March 22 agreement calls for a $3.4 million renovation to begin next month, after Orthodox Easter celebrations. Each religious group will contribute one-third of the costs, and a Greek bank contributed 50,000 euros, or $57,000, for the scaffolding, in return for having its name emblazoned across the machinery.

The idea is to peel away hundreds of years of the shrine’s history, clean it, and put it back together. Simple enough, but delayed for decades because of the complicated, centuries-old rules and minute traditions — called the status quo — that define the way Jerusalem’s holy sites are governed, in which the very act of repairing something can imply ownership.

“One of the serious issues in the church is that the status quo takes place over every other consideration, and it’s not a good thing,’’ said Athanasius Macora, a Franciscan friar. “Unity is more important than a turf war.’’

The inspiration for this unity was the threat of losing it altogether. Alarmed by reports that the shrine was at risk of collapse, the Israeli police barricaded it for several hours on Feb. 17, 2015, throwing out the monks who guard it and preventing hundreds of pilgrims from entering.

The message was clear: Fix it, or else.

So after a year of much study and negotiation, monument conservation experts plan to first remove the iron cage that Jerusalem’s colonial British rulers built in 1947 in a prior effort to keep the Aedicule from collapsing, after a 1927 earthquake and rain left the structure cracked, its marble slabs flaking.

They will take apart, slab by slab, the ornate marble shell built in 1810, during Ottoman rule of Jerusalem. The conservationists will then tackle the remains of the 12th-century Crusader shrine that lies beneath. That was erected after the Shi’ite ruler of Egypt, al-Hakim, destroyed the first Aedicule in 1009. The original was built by Helena, mother of Emperor Constantine, the Christian Roman emperor who did much to elevate the status of Christianity through the empire.

Finally, the workers will repair cracks in the remains of the rock-hewed tomb underneath, where most Christians believe Jesus was placed after he was crucified. (There is a rival Tomb of Christ just outside the Old City walls, patronized mainly by Protestants.)

Antonia Moropoulou, the conservation expert heading the project, said the shrine would remain open to visitors during most of the process.

Hundreds of pilgrims waited to enter one recent day.

“The world cannot give me the feeling I get from this tomb, this place,’’ said Anil Macwan, 30, a lay Catholic preacher from India.