It was a Vatican visit such as no other head of state has ever enjoyed. Instead of greeting him, like all previous high-ranking visitors, in the papal library of the Apostolic Palace, the Pope took Mr Bush round the medieval St John's Tower then gave him a tour of the Vatican gardens, culminating in a brief open-air concert by the Sistine Chapel Choir.

The Pope waited for the President at the entrance of the tower. As he arrived, the President was overheard gushing "What an honour" as the two men disappeared for a half-hour tête-à-tête, details of which have not been made public.

The special reception was seen as a return of favours for the magnificent party thrown for the Pope two months ago when he turned 81 during his US tour, attended by up to 9,000 guests. But yesterday the Vatican was seething at rumours that there was much more to it than protocol: George Bush,lifelong Methodist, was about to convert.

The notion was given extra mileage by the fact that the President's brother Jeb, the former governor of Florida, converted to Catholicism on marrying his wife Columba, a Mexican.

The Vatican differs from the White House on immigration and the death penalty but on other issues including stem cell research, gay marriage and abortion there has been, as the Catholic daily L'Avvenire put it, "total harmony."

Cardinal Pio Laghi, the papal envoy to the White House, said: "Bush believes in the values of the Church and his brother is a convert."