Michael Kelly of the Irish Catholic newspaper asked, "Was Enda Kenny trying to be rude or does he just not know how to behave correctly?
"It's about basic manners and unfortunately Mr Kenny was again found wanting."
Video footage taken by the Italian newspaper Corriere Della Sera from Castel Gandolfo, the Pope’s weekend retreat where the leaders met with him, shows Kenny reading his phone and texting while the Pope speaks.
At one stage, he is apparently taking a photo of Pope Benedict. When the Pope stops speaking, Kenny is slow to react and does not applaud as he has the cell phone in his hand.
The relationship between Kenny and the Vatican has been strained since he unleashed a widely covered attack on their handling of the child abuse issue in Ireland soon after he became Prime Minister.
Kenny was with a group of Christian Democrats leaders from different European countries who were invited to an audience with the Pope, though he did not actually meet him.
Here’s the video of Enda Kenny checking his phone during the speech: