First Minister Carwyn Jones has written to the Pope's representative to Britain pointing out the last papal visit to Wales in 1982 was "a great success".
Mr Jones wrote that it would be a "disappointment for the people of Wales to miss out on this happy and historic event".
Pope Benedict is expected to visit England and Scotland in September.
The first minister wrote: "The last papal visit to Wales in 1982 was a great success. However, that was more than 25 years ago and the political, social and religious landscape of the UK has changed significantly since then.
"In Wales, there have been especially profound changes, not least the advent of the National Assembly for Wales and our growing sense of self-confidence as a nation.
"The traditions of the Catholic Church have remained an abiding feature of our country's life. As we saw in 1982, a papal visit is an occasion of great joy and pride, not only for Wales' Catholic community but also for the whole of our nation.
"I fully appreciate that the Pope will have a very busy schedule during his visit but, as this would only be the second visit by a pontiff to the UK in nearly 500 years, it would be a disappointment for the people of Wales to miss out on this happy and historic event."
In 1982, John Paul II held masses in cities including Cardiff, London, Liverpool, Manchester and Edinburgh, and he also met the Queen and Archbishop of Canterbury.
The first reigning Pope to visit Wales addressed 150,000 people at Pontcanna Fields, starting the mass in Welsh.
He also held a youth service at Ninian Park, the former home of Cardiff City FC.
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SIC: BBC