When a journalist saw on WhatsApp that the pope was trying to contact him on his birthday, he assumed it was a joke. Then he realised that the source of the call was the Vatican, and to his astonishment he soon found himself talking to Pope Francis.

Argentina's Alfredo Leuco is not the first person cold-called by the pope, who continues to endear himself to Catholics and non-Catholics by his accessibility, as unpredictable as it is unprecedented.

The pope already knew and admired Leuco's work but the journalist came to his attention on this occasion by publishing an open letter challenging the Pope's decision to receive Argentine president Cristina Kirchner for a fifth time in the Vatican. Leuco claimed many Argentines were "upset or disillusioned" by the meeting.

"On Saturday I was celebrating my birthday with six of my best friends and partners in the city of San Pedro. At 11.23 I got a first WhatsApp from Monsignor Guillermo Karcher. I thought it was a joke. But when I noticed the number of origin was the Vatican," Leuco revealed on his radio programme. "I had to pinch myself several times to make sure I was not dreaming. I was filled with happiness when Karcher said: 'The pope remembers you and greets you'."

Just after 2pm that day, he "almost died of joy" when he got a voicemail from the pope on his mobile. At about 3pm, the pope called again and got through. Leuco's open letter had caused controversy in Argentina and the journalist himself had been attacked on social media. The pope praised the "moral fortitude" of the letter. He told the pope he was being "slaughtered" on social networks and asked him if he could report the conversation. The pope said yes, and Leuco felt himself almost start to cry.

The pope ended by saying: "I wish you a good birthday party and do not forget to pray for me." Leuco said he felt ashamed. "I did not dare to tell him that I knew not how to pray." He then decided to ask a couple of rabbis he knows to teach him how to pray so he could fulfil the pope's request.

On his blog, he wrote later: "I say and I repeat and still I can not believe it. But it is absolutely true. Wonderfully true. This is the greatest achievement of my journalistic life: Pope Francis did me the honour to answer, with great affection and gratitude, the open letter read on this radio that had such an impact that it became one of the most discussed topics on Twitter."

His open letter had been strongly critical of Kirchner. It is a sensitive time because Argentina has a general election in October. Technically, Kirchner cannot run for a third time but many of her supporters want the rules changed to permit this.