Cherie Blair, a Catholic, who was accompanied by two of the four Blair children, Kathryn and Leo, spent only a few minutes with the Pope as gifts were exchanged before the two men held talks in the papal library with nobody else present.

The prime minister presented the Pope with two CDs of music by Mozart, the pontiff’s favourite composer, and a pair of silver cufflinks.

Once talks got under way, they were described by Downing Street as a “dynamic discussion”, a possible reference to contrasting views.

The Pope made it clear he wanted to see “an open and constructive dialogue” to resolve tension over Iran’s nuclear plans and that he was convinced the stand-off could be resolved by diplomacy.

The pair also discussed how the “moderate voices” of leading faiths need to stand up to extremism and terrorism.

A Vatican source said Blair endorsed an invitation by British bishops to the Pope to visit Britain. It is possible such a visit could include a trip to Northern Ireland, the first to the province by a pope. The most likely venue would be Armagh, where there are Roman Catholic and Church of Ireland cathedrals.

At a separate meeting after the audience with the pontiff, Blair met Cardinal Angelo Sodano, Vatican secretary of state, who told him Benedict was “looking warmly” on the British invitation.

The Blair family also visited the tomb of John Paul II in St Peter’s and said prayers.

Blair’s last papal audience was in February 2003, when he met John Paul II to explain why he believed a military attack on Saddam Hussein would be justified.

A Downing Street spokesman said: “There is an open invitation for the Pope to visit the UK. As far as dates are concerned, we don’t get into that kind of detail.”

The Blairs were returning to Britain last night at the end of a week’s holiday in Italy during which the prime minister also met Romano Prodi, his new counterpart.

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