VATICAN CITY — Pope Francis indicated his willingness to visit North Korea during a private audience with South Korean President Moon Jae-in at the Vatican, Moon’s office said Thursday.

The South Korean presidential office said in a statement that Moon “conveyed North Korean leader Kim Jong Un’s desire for a papal visit to North Korea.” A formal invitation directly from North Korea will follow.

The office said Francis responded that “if the invitation comes, I will surely respond to it, and I can possibly go.”

Moon’s office revealed last week that Kim had indicated his desire for a papal visit during a Korean summit last month.

If it materializes, such a visit would be the first by a pope to the atheist country.

The private audience lasted 35 minutes, and included an exchange of gifts. Moon, who is Catholic, presented the pope with a relief of the face of Jesus Christ by a Korean artist. The president pointed to the wreath of thorns on Jesus’ head, telling the pontiff: “This represents the suffering of the Korean people.”

The pope’s gifts included a medal engraved with an olive branch, saying it represented “his desire for peace” on the Korean peninsula.

During their exchange, Moon told the pope that “you are not only the head of the Catholic Church, but a teacher for humanity.” Francis urged Moon to “work for peace.”

Moon on Wednesday met with Italian leaders and attended an evening Mass for peace in St. Peter’s Basilica with the Vatican’s top diplomat, Cardinal Pietro Parolin.

Moon signed a broad agreement with North Korea’s Kim last month meant to reduce military tensions on the peninsula. The South Korean President wrote in the Vatican newspaper, L’Osservatore Romano, that he traveled with a Korean Catholic bishop to try to improve relations between the Church in the North and South.

North Korea strictly controls the religious activities of its people, and a similar invitation for then-Pope John Paul II to visit after a 2000 inter-Korean summit never resulted in a meeting.

The Vatican insisted at the time that a papal visit would only be possible if Catholic priests were accepted in North Korea.

Francis, however, has taken a more open approach in the Holy See’s diplomacy.