ROME — Pope Francis had quite a 78th birthday. The pontiff began Wednesday with prayers and a birthday celebration with tango dancers near St. Peter’s Square. His day ended with a historic diplomatic breakthrough between Cuba and the United States — and the disclosure that the Argentine pope played a key role as broker.

Francis is being credited for helping bridge the divide by first sending letters to President Obama and President Raúl Castro of Cuba, and then having the Vatican host a diplomatic meeting between the two sides in October.

“The Holy Father wishes to express his warm congratulations for the historic decision,” Francis said in a statement issued Wednesday night by the Vatican.

Vatican spokesmen declined to provide any details about Francis’s letters, other than that he encouraged the two sides to resolve “humanitarian questions”; resolve the release of political prisoners, including an American held by Cuba, Alan P. Gross; and “initiate a new phase in relations.”