He suggested that the Church should act as a "critical friend" of the NHS, "not as a critic standing over the NHS in judgement".
His comments followed a report that found 14 NHS Trusts to be "trapped in mediocrity".
The report, the Keogh review, published on Tuesday, was commissioned by the Government in February, in re- sponse to the publication of the Francis report into the Mid Staffordshire NHS Foundation Trust, which uncovered "appalling" standards of care there.
Professor Sir Bruce Keogh, the NHS medical director, was asked to investigate Trusts that had persistently high mortality rates. His said he was confident that "mediocrity" in the 14 Trusts named could be "replaced by a sense of ambition".
The report found in the Trusts a "limited understanding" of the importance of listening to patients and staff; a lack of value of, and support for, front-line clinicians; and transparency used "for the purpose of accountability and blame, rather than support and improvement".
In several cases, action taken at once to protect patients had in- cluded the immediate closure of operating theatres, and changes to staffing levels. Shortage of nurses was a problem. At Burton Hospitals NHS Foundation Trust, staff were working for 12 days in a row without a break.
All but two Trusts had had "never events": serious, largely preventable, patient-safety incidents. There had been 12 such events in three years at United Lincolnshire Hospitals NHS Trust.
The Health Secretary has been accused of seeking to gain political capital from the report.
On Tuesday, Mr Hunt told the House of Commons: "The last government left the NHS with a system that covered up weak hospital leadership, and failed to prioritise compassionate care. The system's reputation mattered more than individual patients; targets mattered more than people."
The Shadow Health Secretary, Andy Burnham, said that this "partisan statement" was "not worthy" of Sir Bruce's "excellent" report, which was "about the Right Hon. gentleman's Government, and failings that are happening now, on this Government's watch." The Government, he said, was conducting "cynical spin operations".
On Wednesday, Bishop Newcome said: "It's a great pity when health becomes over-politicised. Because, actually, what we are concerned about is individual people and their families; and I would have thought that everybody shared a concern for their well-being and welfare. The NHS is a great institution which we want to preserve and maintain at all costs, and we are just jolly fortunate to have it. It should be the one area where politicians should be able to work together for the well-being of the country, rather than endlessly engaging in slanging matches about who is to blame."
One of the 14 Trusts investigated by Sir Bruce, North Cumbria University Hospitals NHS Trust, is in the diocese of Carlisle. Bishop Newcome said that the diocese's invitation to all NHS staff to attend "stress relief days" at its retreat centre, Rydal Hall, had been "very successful". He could relate to Sir Bruce's observations about the difficulty of recruiting staff to geographically remote areas.
On Wednesday, the Revd David Flower, Principal Chaplain at Colchester Hospital University Foundation Trust, another hospital mentioned in the review, but one not placed in special measures, said that the review's diagnosis of a failure to listen to patients and staff was not "typical" of his Trust.
"We are encouraged to be involved in active listening, with clergy chaplains and volunteer lay chaplains, with patients, staff, and relatives. We are also encouraged to be part of multi-disciplinary meetings, and part of ward teams. We are also encouraged to attend training meetings with other chaplains, and in personal reflection. We feel very supported by senior managers and the Trust Board. The chaplaincy team feels it is in a strong place to influence this organisation."