The fire is a "catastrophe for France, for Spain and for Europe," Spanish Prime Minister Pedro Sánchez tweeted Monday, adding that the flames are destroying "850 years of history, architecture, painting and sculpture."
French President Emmanuel Macron told reporters near the scene that he will seek international help, including from the "greatest talents" in the world, to rebuild Notre Dame.
"It's a part of our growing up, it's a part of our culture, it's a part of our lives," Trump said of the landmark.
The Notre Dame Cathedral, situated on an island in the Seine River in the heart of Paris, is one of the world's most visited tourist destinations, drawing some 13 million people each year. The fire's emotional impact was widely felt. People from all over described in Facebook posts how they cried when they heard about the fire.
"The majesty of Notre Dame - the history, artistry, and spirituality - took our breath away, lifting us to a higher understanding of who we are and who we can be," she tweeted. She predicted the cathedral would rise again.
Japan's government early Tuesday expressed sympathy and said it would consider sending support to the French government. "Its damage is a loss to the world and our hearts ache," said Yoshihide Suga, the chief cabinet secretary.
The Vatican said Pope Francis "has seen with shock and sadness the news of the terrible fire."
As the flames spread, Cardinal Timothy Dolan, the archbishop of New York, prayed at St. Patrick's Cathedral in Manhattan for intercession.
"God preserve this splendid house of prayer, and protect those battling the blaze," Dolan said in a statement.
Paris Mayor Anne Hidalgo said many works of art and holy objects inside the church had been saved, but the art world was distressed about what might have been lost.
Barbara Drake Boehm, senior curator at the Metropolitan Museum of Art's medieval Cloisters branch in New York, was desolate about damage to the cathedral, which she called "one of the great monuments to the best of civilization."
"Civilization is just so fragile," Boehm told a reporter in a trembling voice. "This great hulking monument of stone has been there since 1163. It's come through so many trials."
Jeff Ament, bass player for Pearl Jam, remembered spending hours at the cathedral in his first visit, in 1991, with record executive Michael Goldstone.
"Thinking about Paris," Ament tweeted, with photos of the cathedral.
U.N. Secretary-General Antonio Guterres tweeted that he's "horrified," calling the cathedral "a unique example of world heritage."
In Russia, the Russian Orthodox Church's secretary for inter-Christian relations Hieromonk Stefan called the fire "a tragedy for the entire Christian world and for all who appreciate the cultural significance of this temple," the state news agency RIA-Novosti reported:
On Twitter, Trump suggested using planes to drop water on the flames. France's Civil Security agency said that wasn't feasible.
"All means are being used, except for water-bombing aircrafts which, if used, could lead to the collapse of the entire structure of the cathedral," the agency tweeted.
Associated Press reporters Jocelyn Noveck and Kiley Armstrong in New York, Jim Heintz in Moscow, Edith M. Lederer at the United Nations, and Samuel Petrequin in Paris contributed to this report.
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