The unprecedented gesture came as his incoming number two, the Vatican's newly-nominated secretary of state, said that the rule that priests should be celibate was not "a dogma of the Church" and could be open for discussion.
Francis, who has won praise for spontaneous and unusual moves during his six month papacy, wrote a lengthy letter to a newspaper, La Repubblica, which the Italian daily printed over four pages, including page one, under the simple byline "Francesco".
"God forgives those who obey their conscience," he wrote in the unprecedented letter, the latest example of the markedly different tone and style from his predecessors that he has set since being elected in March.
The 76-year-old pontiff was responding to editorials written in July and August by Eugenio Scalfari, an agnostic and the paper's founder, in which he was asked whether "the Christian God forgives those who do not believe and do not seek faith".
Mr Scalfari said he had not expected the South American pope to respond "so extensively and so affectionately, with such fraternal spirit".
The Pope wrote: "The question for those who do not believe in God is to follow their own conscience. Sin, even for a non-believer, is when one goes against one's conscience.
"To listen and to follow your conscience means that you understand the difference between good and evil."
He said that the "mercy of God has no limits" and encompassed even non-believers, but his remarks failed to impress the Italian Union of Atheists and Agnostics.
"Why should a non-believer seek legitimisation from the Pope?" the association asked.
It dismissed what it called the pontiff's "nice words" and said: "What interests non-believers is certainly not 'forgiveness' from an entity whose existence we do not trust."
The Pope's reaching out to atheists echoes a homily he delivered in May, when he said that even atheists could be welcomed into heaven. That declaration caused consternation among Vatican officials, with a spokesman later appearing to backtrack on the Pope's remarks, saying that people who do not believe in God "cannot be saved".
In a further sign that the Church is edging towards more openness, Archbishop Pietro Parolin, a Vatican diplomat who will next month become the Pope's deputy as secretary of state, said that the principle of celibacy among clergy was "ecclesiastical tradition" rather than "Church dogma" and therefore open to discussion.
The Pope has struck a more inclusive tone since taking over as leader of the world's 1.2 billion Roman Catholics in March, notably reaching out to homosexuals on his return from a week-long trip to Brazil in July.
"If someone is gay and he searches for the Lord and has good will, who am I to judge?" the Pope said.