To answer this question, it's important to keep in mind that "The Cask of Amontillado" by Edgar Allen Poe is a dark tale of revenge. This is clear from the narrator's very first line:
The thousand injuries of Fortunato I had borne as I best could, but when he ventured upon insult, I vowed revenge.
However, the narrator wants not only to be avenged, but to punish Fortunato. For this reason, he creates an elaborate ruse to lure him into the dark catacombs by pretending to be his friend. As he says,
I continued, as was my wont to smile in his face, and he did not perceive that my smile now was at the thought of his immolation.
In other words, he smiles at Fortunato to deceive him, all the while plotting to murder him.
The narrator uses the guise of friendship, as well as the promised Amontillado, to persuade the drunken Fortunato to accompany him. When they first meet he calls him "my dear Fortunato" and then appeals to his vanity by suggesting that he needs his assistance as a connoisseur of fine wines. In this way he draws him into the damp cellar vaults. He tricks Fortunato further by pretending to persuade him to go back, knowing that he will all the more insist on continuing.
When they pass the nitre that causes Fortunato to break forth into a fit of coughing, the narrator says: "My poor friend found it impossible to reply for many minutes." When he writes this, he is being ironical. In other words, he is saying the opposite of what he truly means. When he refers to his "poor friend" he really means "helpless victim." Remember, he is writing this account after he has already committed the crime, and so he is addressing his presumed readers, who are already aware that he is intending revenge. The story takes on the nature of a confession, although the narrator does not seem at all repentant.