Rome (CNN) -- French President Francois Hollande met with Pope Francis privately Friday amid media speculation over his alleged affair with an actress.
Hollande also plans to meet Vatican Secretary of State Pietro Parolin and French clergy while in Rome.
Hours before he arrived at the Vatican, a small bomb exploded in central Rome near a French foundation and French cultural center, police said.
The blast damaged three cars and broke windows in two nearby buildings, said Agostino Vitolo, a spokesman for Italy's military police, or Carabinieri.
There's been no claim of responsibility for the bomb. It's unclear whether its detonation is linked to the visit by the French President.
Hollande's private life has been the subject of global headlines since claims in the French magazine Closer of a two-year affair with actress Julie Gayet.
The allegations of an affair have left the position of the President's partner, Valerie Trierweiler, in some doubt.
It's not clear whether she will accompany Hollande on a state visit to Washington next month.
Hollande and Trierweiler are working to issue a "clarification" concerning their relationship, Trierweiler's attorney, Frederique Giffard, told the French daily newspaper Le Figaro in an interview published late Thursday.
After the alleged love affair, Trierweiler "truly wants to resolve the matter in order to come out of it in the most dignified way possible," Giffard told Le Figaro.
Trierweiler has been Hollande's partner for several years.
Last weekend, she left the hospital where she'd spent a week being treated for stress and fatigue, Paris Match magazine reported. The same magazine -- where Trierweiler is a longtime correspondent -- said Saturday that she would recover for "several days" in an official residence in Versailles.
Hollande may hope his visit to Rome will help improve his standing in France, a majority-Catholic country.
His relationship with many Catholics was damaged by a bruising battle last year over the passage of a law allowing same-sex marriage and adoption. The measure was one of Hollande's election pledges.
The Catholic Church in France opposed the legislation. Many of the faithful joined huge marches in protest against it, but they were unable to stop it from becoming law.
Nationwide, Hollande has seen his personal approval ratings plummet since his election in 2012, although this has been attributed to dissatisfaction with his leadership rather than disapproval of his private life.
A recent survey by French pollster Ifop with French newspaper Le Journal du Dimanche found that more than 80% of respondents had not changed their opinion of the President based on the allegations of an affair.
CNN's Livia Borghese reported from Rome, and Laura Smith-Spark wrote and reported in London. CNN's Pierre Meilhan contributed to this report.