Culture Minister Franck Riester breathed a huge sigh of relief, telling reporters outside Notre Dame that the nation's "most precious treasures" were largely spared.
Many of the works will be stored at Paris' City Hall and the Louvre, where they will be examined, treated for damage and protected, officials said.
Audrey Azoulay, director-general of UNESCO, the U.N. culture agency, said Notre Dame has "a particular place in the world's collective imagination" and has pledged her agency's help to rebuild.
Monday's fire almost destroyed the entire cathedral, which has stood in Paris and survived nearly 900 years of tumultuous French history.
Paris prosecutor Remy Heitz has launched an investigation, which he said would be "long and complex."
So far, authorities have said the blaze appears to be an accident, possibly connected to a multimillion-dollar renovation project being carried out by five companies.
"Nothing suggests that it was a voluntary act," Heitz told reporters outside the cathedral Tuesday.
An initial fire alert was sounded at 6:20 p.m. local time Monday, but no flames were found, according to Heitz. The second alert was sounded at 6:43 p.m., when flames were spotted on the roof. It was nine more hours before the flames were finally extinguished.
The Crown of Thorns was recovered when Paris fire chaplain Jean-Marc Fournier accompanied firefighters into the burning cathedral to recover the ancient relic, said Philippe Goujon, mayor of Paris' 15th District.
Let our news meet your inbox. The news and stories that matters, delivered weekday mornings.
The artifact, which was brought to Paris by King Louis IX in the 13th century, is purported to have been pressed on to Jesus' head during the crucifixion.
Le Grand Orgue, or "the great organ," and its 8,000 pipes also survived, authorities said. The instrument, which dates to the 1730s, was constructed by Francois Thierry.
The organ is "a very fragile instrument, especially its pipes," according to Bertrand de Feydeau, vice president of the preservation group Fondation du Patrimoine.
"It has not burnt, but no one can tell whether it has been damaged by water. Nobody knows if it is (in) a functioning state or will need to be restored," de Feydeau said.
A famed piece of stained glass known as the South Rose window also survived, as did the Tunic of Saint Louis, a long, shirt-like garment from the 13th century, officials said.
"The crown of thorns, the tunic of St. Louis and many other major artifacts are now in a safe place," Paris Mayor Anne Hidalgo tweeted, thanking first responders for their work in saving the treasures.
Sixteen copper statues of saints that could have been in harm's way Monday had been removed just days earlier as part of the restoration efforts.
The church's roof, known as The Forest because of its long planks of centuries-old wood, collapsed in the blaze and cannot be rebuilt in its original form, officials said. That's because France no longer has oak trees big enough to replace the ancient wooden beams that burned.
"We don't, at the moment, have trees on our territory of the size that were cut in the 13th century," de Feydeau told France Info radio.
The spire was the most visible victim of Monday's fire, with Parisians watching in horror and tears as the famed structure succumbed to the flames.
The 13th-century spire was dismantled during the French Revolution before it was rebuilt in the 1860s.
Also believed lost are statues of St. Denis and Ste. Genevieve, the patron saints of Paris, as they had been stored in the spire.
"They were placed at the summit of the church in 1935 by the archbishop of Paris to protect the building," said Laurent Ferri, the former heritage conservator at the French National Archives. "If so, they are now likely reduced to ashes. It is a great loss for Catholics and for art lovers worldwide."
Officials could not immediately say Tuesday whether the "True Cross" — a 9.45-inch part of the cross that the church says Jesus was crucified on — survived the blaze.
The fate of a 3.5-inch-long nail said to have been used in the crucifixion, which was inside the cathedral, was also unknown.
Priceless art adorned many walls inside the cathedral, including the 1648 "Saint Thomas Aquinas, Fountain of Wisdom," by Antonie Nicolas, and the 1716 "The Visitation," by Jean Jouvenet. It was not immediately known whether they perished or were saved.
It also was not clear whether a famed 14th-century life-size statue of the Virgin Mary and the baby Jesus survived the blaze.
David K. Li
David K. Li is a breaking news reporter for NBC News.