South Korea's president has met with Pope Francis in a private audience, and his office says that the pontiff indicated his willingness to visit North Korea.

The South Korean presidential office said in a statement Thursday that President Moon Jae-in "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 said that "if the invitation comes, I will surely respond to it, and I can possibly go."

Kim initially indicated his desire for a papal visit during a Korean summit last month.

If it materialises, such a visit would be the first by a pope to North Korea.