Carla Bruni has announced the baby name for her first child with husband Nicolas Sarkozy, president of France.
"Giulia" is the baby's name, Bruni said on her official website.
Bruni, who was born in Turin, Italy, said she was "very touched" by all the congratulatory messages received since the birth of Giulia on Wednesday at a Paris clinic.
"I am deeply touched by the many messages of congratulations that I have received since the birth of our daughter Giulia," Bruni said.
"On this happy occasion, my husband joins me in warmly thanking all those of you who sent us these tokens of your kindness."
A middle name for the baby has not been announced.
Giulia is the Italian version of the girl's name "Julia." Actress Debi Mazar also has a daughter named Giulia.
Sarkozy earlier Thursday responded to media questions by saying his wife would reveal the name of their baby girl, who was born Wednesday evening at a Paris clinic.
Sarkozy commented on his wife and baby girl for the first time Thursday morning.
"They are doing very well," Sarkozy said, according to French newspaper Le Figaro.
He told reporters that Bruni would reveal their daughter's name, and described the birth as a "very profound joy, a joy all the deeper because it is private," BBC News reports.
Rumors abounded throughout the day about possible names for the baby, with "Julia," "Dalia" and 'Dahlia" among the guesses.
More from GlobalPost: Carla Bruni gives birth to baby girl (PHOTOS)
Sarkozy stopped in to visit his wife and new daughter at the maternity clinic on Thursday, Agence France-Presse says.
He was also at the clinic on Wednesday but left after 20 minutes in order to travel to Frankfurt for eurozone debt talks, according to BBC News. He returned to his wife a few hours after the birth.
More from GlobalPost: Sarkozy flies to Frankfurt for eurozone talks
Security is tight at the clinic in western Paris, which is surrounded by photographers under huge pressure to get the first shot of Baby Bruni-Sarkozy, the Guardian reports.
Crowds of well-wishers have gathered outside the clinic, and a security cordon had to be set up, according to the BBC.
Bruni, 43, has a son named Aurelien from a previous relationship, while Sarkozy, 56, has three sons from earlier marriages.
More from GlobalPost: French Socialists choose "Monsieur Normal" Francois Hollande to challenge Sarkozy