Francis thanked medical personnel working for the Catholic Church who "care for those suffering from HIV/AIDS" and praised "all who strive diligently to educate people in the area of sexual responsibility and chastity," the Vatican said in a statement.
"By promoting prayer, marital fidelity, monogamy, purity and humble service of one another within families, the Church continues to make an invaluable contribution to the social welfare of Tanzania," he said.
AIDS campaigners often disparage the Catholic Church for not recognising the use of condoms as a means of preventing the spread of the virus.
Francis's predecessor Benedict XVI was heavily criticised for saying during a trip to Africa that the distribution of condoms "aggravates" the AIDS crisis.
But in a book of interviews in 2010, he gave a more considered answer, saying that "condoms alone do not resolve the question".
He also gave the example of a male prostitute choosing to use a condom to prevent HIV infection as a "first step in a movement toward a different way, a more human way, of living sexuality".