"We feel if the Prime Minister herself was to visit that, she would also experience that. The experience of the land and the people would be very helpful to a just resolution."
Sullivan said Pope Francis has made the Catholic Church's position on issues like Ihumātao very clear.
"That [position] is one of strong support for the rights of indigenous peoples, for the retention of their land and cultures. That has certainly happened in this country."
Demonstrators walked from Ihumātao to Ardern's electorate office in Mt Albert on Thursday with a 26,000 signature petition asking her to visit the site.
However, Ardern was not in Auckland to receive the petition and said a visit would be distraction from the negotiations being led by the Māori King.
"Visiting doesn't get us closer to a resolution. It ultimately needs to come from mana whenua. I haven't ruled out visiting in the future, but right now I see it as a distraction to finding a resolution," she said.
There have been suggestions the wealthy Tainui iwi, who have a connection to the whenua, could buy the land.