Hours after his birth, a picture of Kareena planting a kiss on his newborn's forehead started doing rounds on social media.
But when ABP News buzzed Kareena's PR, they clearly denied it and termed the picture as fake.
Kareena, daughter of veteran actors Randhir Kapoor and Babita, delivered the baby on Tuesday morning at the Breach Candy Hospital here.
A statement released on behalf of the actors read: "We are very pleased to share with you all the wonderful news about the birth of our son: Taimur Ali Khan Pataudi, on December 20, 2016.
"We would like to thank the media for the understanding and support they have given us over the last nine months, and of course especially our fans and well wishers for their continued affection. Merry Christmas and a happy new year to you all...With love, Saif and Kareena."
Kareena and Saif, who have worked together in films like "Tashan", "Kurbaan", "Agent Vinod", LOC Kargil" and "Omkara", got married in October 2012.
Saif, the son of veteran actress Sharmila Tagore and the late Mansoor Ali Khan Pataudi, was earlier married to actress Amrita Singh and shares two children with her - daughter Sara and son Ibrahim.
He is doing "extremely well" after becoming a father again, says his sister Soha Ali Khan.