King Charles and his wife Queen Camilla's state visit to the Vatican has been postponed because of medical advice that suggested Pope Francis would benefit from an extended period of rest, Buckingham Palace said on Tuesday.

The British royals were due to travel out to the Vatican on April 7 and meet Pope Francis the following day, for what the palace had said would be a historic visit.

Days after the plans were first announced last month Francis, 88, was admitted to hospital with a severe respiratory infection and he was only finally discharged on Sunday, after the most serious health crisis of his 12-year papacy.

A royal source said last week Charles and Camilla were hoping and praying that the pope's health would improve enough to allow the trip to go ahead, but it has now been called off by mutual agreement.

"Their majesties send the pope their best wishes for his convalescence and look forward to visiting him in the Holy See, once he has recovered," the palace statement said.

The royal couple's subsequent state visit to Italy is set to continue but the programme might now be subject to changes.

Francis was admitted to Gemelli hospital on February 14 for a bout of bronchitis that developed into double pneumonia, an especially serious condition for him, as he had pleurisy as a young adult and had part of one lung removed.

The head of the pope's medical team said he came close to death at one point during his hospitalisation.

Charles, 76, also has his workload carefully managed as he recovers from cancer.