Bishop Michael Dooley said prayers were said across Dunedin during Masses yesterday.
"People are probably concerned because he’s a bit like a grandfather or something like that who may not be long with us."
The Vatican released a statement on Saturday indicating Pope Francis’ condition had deteriorated.
The 88-year-old Pope was admitted to Rome's Gemelli hospital on February 14 with a respiratory tract infection, it said.
He was subsequently diagnosed with pneumonia in both lungs.
The statement said the leader of the Catholic Church had gone through several blood transfusions and required high level oxygen support to breathe, in what was described as a "respiratory crisis".
"The Holy Father’s condition remains critical.
"The Pope is not out of danger."
Bishop Dooley said although many Catholics "feel for" the ill Pope, many were also probably thinking if it was his time to go "then that’s his time".
He believed the Pope’s attitude would be similar.
Pope Francis would remain the leader of the church until he died or resigned, Bishop Dooley said.
However, he did not think the Pope would resign, rather he would "just carry on until he died".
"He would have to [resign] himself and I don’t see how that would help things at all when he could die imminently."
People would be happy if the Pope made a full recovery but understood that double pneumonia could be fatal for the 88-year-old.
A cardinal in Rome would look after the general running of the Catholic Church while the Pope was in hospital.
Bishop Dooley met Pope Francis in 2019 for an hour and 20 minutes when five bishops from New Zealand travelled to Rome for 10 days.
He said he was very approachable.
"He was very easy to talk to and very interested in New Zealand.
"He was a bit like a parish priest, he was concerned about the people."
Double pneumonia is a serious infection that can inflame and scar both lungs, making it difficult to breathe.
Reuters said the Vatican had described the Pope's infection as "complex," saying it is was caused by two or more micro-organisms.
The Pontiff from Argentina needed blood transfusions because tests showed he had a low platelet count, which is associated with anaemia.
It was announced earlier on Saturday the Pope would not appear in public yesterday to lead prayer with pilgrims for the second consecutive week.
It was believed to be the first time he had missed two consecutive Angelus prayers for health reasons.
In a briefing on Friday, two of his doctors said the pope was highly vulnerable due to his age and frailty.
Dr Sergio Alfieri, a senior member of the Gemelli staff, said there was a risk the lung infection could spread to his bloodstream and develop into sepsis, which "could be very difficult to overcome".
Francis, who has been Pope since 2013, has suffered bouts of ill health in the past two years.
He is particularly prone to lung infections because he developed pleurisy as a young adult and had part of one lung removed.
Argentina issued a nationwide call earlier in the week to all "villas" and "barrios" — poor neighbourhoods and towns — to pray for the pontiff.
The previous Pope, Pope Benedict XVI was elected in 2005 and resigned in 2013, citing a "lack of strength of mind and body".
He died in 2022 aged 95.
