Prime Minister Peter O'Neill made the invitation during a meeting with Port Moresby archbishop John Ribat, who is soon to be elevated as Papua New Guinea's first cardinal, and archbishop Kurian Mathew Vayalunkal, the new Apostolic Nuncio to Papua New Guinea and Solomon Islands.
"I asked the Apostolic Nuncio to pass on our thanks for elevating one of our sons to such an important position in the Catholic Church.
"This is an honuor for our people and we are proud of our first cardinal.
"Following cardinal Ribat's elevation, I hope we will be able to receive Pope Francis in Papua New Guinea.
"Pope John Paul II visited Papua New Guinea on two occasions and people of all Christian denominations in our country would like to welcome His Holiness, Pope Francis.
"A Papal visit brings people together, and unites them through commitment to God and Church, regardless of which denomination they are from," O'Neill said.
Archbishop Vayalumkal recently arrived in Papua New Guinea to begin his appointment. He has been with the Diplomatic Corps of Vatican since 1998 and worked in Hungary, Korea, Dominican Republic, Egypt and Bangladesh in his diplomatic capacity.
He also served in Haiti after a large earthquake in 2010 to oversee the humanitarian work taken up by the Vatican.