He condemned “terrible forms of exploitation, unworthy of humanity” in Congo, where vast mineral wealth has fuelled war, displacement and hunger.
The Congolese, the pope said in his homily, were suffering from “wounds that ache.”
After the morning mass, Pope Francis in the afternoon was due to meet victims of violence brought to Kinshasa from the east of the country.
The Pope said that the criminalisation of homosexuality was “unjust.”
Mr Achi was set ablaze by angry bandits after they were unable to gain entry to the parish residence where he dwelled.
The president lauded the deceased for advancing inter-faith dialogue and peace, adding that he will be remembered as a true servant of God.
Pope Benedict’s health had worsened in recent times due to his advanced age.
Pope Francis has urged people to celebrate Christmas more modestly and donate their savings to Ukraine.
The Catholic Church teaches that only men can become priests because Jesus chose men as his apostles.
Asked if he will raise human rights concerns during the visit, Vatican spokesman Matteo Bruni cited Francis’ frequent calls for religious liberty and interfaith dialogue.