Another cardinal, Gianfranco Ravasi, was asked earlier on Thursday if Francis might decide to follow in the footsteps of Pope Benedict XVI and step down if he becomes too ill. Benedict became the first pope in 600 years to retire when he decided in 2013 that he wasn't strong enough to carry on.
Cardinal Ravasi was quoted as telling RTL 102.5 radio: "There is no question that if he [Francis] was in a situation where his ability to have direct contact (with people) as he likes to do... was compromised, then I think he might decide to resign.".
The Pope's overall condition is "improving slightly" and his heart is working well, as he continues hospital treatment for double pneumonia, the Vatican has said.
Mr Bruni said that after waking on Thursday, Francis got out of bed and had breakfast in an armchair, before working from his hospital room with his aides.
Cardinal Juan Jose Omella Omella, his counterpart from Barcelona, emphasised that church life continued even with Francis in the hospital.
