Pope Francis approved a new three-year process to consider reforms for the global Catholic Church, the Vatican said on Saturday, in a sign the 88-year-old pontiff plans to continue on as pope despite his ongoing battle with double pneumonia.

Francis has extended the work of the Synod of Bishops, a signature initiative of his 12-year papacy, which has discussed reforms such as the possibility of women serving as Catholic deacons and better inclusion of LGBTQ people in the Church.

The synod, which held an inconclusive Vatican summit of bishops on the future of the Church last October, will now hold consultations with Catholics across the world for the next three years, before hosting a new summit in 2028.

Francis approved the new process for reforms on Tuesday from Rome's Gemelli hospital, where he is being treated, the Vatican said on Saturday.

The pope has been in hospital for more than a month and his prolonged public absence has stoked speculation that he could choose to follow his predecessor Benedict XVI and resign the papacy.

But his friends and biographers have insisted he has no plans to step down, and the approval of a new three-year process indicated he wants to continue on, despite his age and the possibility he might face a long, fraught road to recovery from pneumonia, given his age and other medical conditions.

"The Holy Father ... is helping push the renewal of the Church toward a new missionary impulse," Cardinal Mario Grech, the Church official leading the reform process told the Vatican's media outlet. "This is truly a sign of hope."

After last October's inconclusive Vatican summit, which yielded no concrete action on possible reforms, Francis had faced questions of whether his papacy was running out of steam.

Vatican officials had said at the time that Francis was still considering future changes, and was waiting to receive a series of ten expected reports about possible reforms this June.

The latest medical bulletins from the Vatican on the pope's condition in hospital have said he is improving and is no longer in immediate danger of death.

They have not said when he will be discharged from hospital.

Well-wishers have been gathering to offer support for Francis outside the hospital each day during the pope's recovery.

Stefania Gianni, an Italian being treated for cancer at the facility, said on Saturday that Francis "has taken great steps to bring the Church up to date with the times".

"He is a great man and a great pope, and the Church still needs him," she said.