Obama made the gesture ahead of a difficult G20 summit hosted by Sarkozy in Cannes, and on Friday he is due to make an unprecedented joint appearance alongside his counterpart on French television.

“I want to congratulate Nicolas and Carla on the birth of Giulia,” Obama said, referring to Sarkozy’s supermodel-turned-singer wife Carla Bruni-Sarkozy, who last month gave birth to the couple’s first child together.

“And I informed Nicolas, on the way in, that I am confident that Giulia inherited her mother’s looks rather than her father’s,” Obama joked to muted laughter from reporters and a rueful smile from Sarkozy.

Obama and his wife Michelle have two daughters, who did not make the trip.

“You can see Barack Obama’s great influence. It’s been four years that he’s been telling me that being a father of daughters is fantastic, he who has two. So I listened to him and followed his example,” Sarkozy said.

Sarkozy has three sons from previous marriages, and Bruni-Sarkozy one. The couple has been very discreet in public about Giulia’s birth, having promised not to use her as an electoral prop.

The French and US leaders have not always enjoyed such warm relations, after Obama rebuffed Sarkozy’s initial attempts to forge a privileged relationship in the first months after his election.

But Friday’s television appearance, which will follow a joint meeting with French troops in the wake of the NATO campaign in Libya, appears to mark a warming in ties.