"God's mercy has no limits if we turn to him with a sincere and contrite heart," the leader of the world's 1.2 billion Catholics said in a missive published in La Repubblica by its founder Eugenio Scalfari.
"The question for people who do not believe in God is to listen to their consciences. Also for those without faith, sin is going against your conscience," he said.
"Listening to it and obeying it means making up one's mind about what is good and evil," he added.
Since being elected in March, the Argentine pope has repeatedly said he wants his words to be heard by faithful from other religions and non-believers.
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During a blessing in St Peter's Square in May, Francis said non-believers could be redeemed just like Catholics -- an unusual message that was quickly denied by a Vatican spokesman who said that anyone who refuses the Catholic Church "cannot be saved".
"The Lord has redeemed all of us, all of us, with the Blood of Christ. All of us, not just Catholics. Everyone! 'Father, the atheists?' Even the atheists. Everyone!" the pope said in his address in May.