Minutes before Sunday Mass at St. Martin of Tours Roman Catholic Church in the Bronx, as the music began, a man approached the Rev. Cosme Fernandes.

“Good morning, Father,” the man said. “I used to live in this neighborhood and I just drove in a truck full of clothes, but they told us they can’t take any more donations. What do I do?”

Father Fernandes had no answer for the man, who had brought the donations for the survivors of a fire that killed 12 people on Thursday. The fire, the deadliest in New York City in more than 25 years, destroyed an apartment building in the mostly-immigrant neighborhood of Belmont, two blocks from the church.

A collection drive organized by the Police and Fire Departments turned into a remarkable outpouring of support that was ended after just one day because of the overwhelming response. On Sunday, people were turned away.