One threat, received from an anonymous caller while President Francois Hollande met with Pope Francis, said a bomb was beneath a 17th century colonnade at St. Peter's Square in Vatican City, the Italian news agency ANSA reported.
The report did not indicate if an explosive device was found.
Earlier Friday, an explosive damaged several cars in central Rome. Another bomb detonated outside a foundation linked to France's embassy to the Vatican.
No one was reported injured in either blast.
During his private visit with Hollande, the pope joked he and the French president shared the same name. Francis is Francois in French.
When Hollande gave the pope a book about St. Francis of Assisi, Francis told him "this is your patron too."
The men talked for about 35 minutes with the help of an interpreter.
Afterward, Hollande met with Vatican secretary of state Pietro Parolin, a cardinal-designate, Vatican Radio reported.