During his interrogation, the man said he was heading to the US embassy to seek asylum when he was arrested, according to the official statement.
The Ministry of Interior, which manages all security services, said the 49-year old suspect, entered a downtown hotel Sunday, tossed a suitcase containing explosive materials out of the window at the synagogue across the street before fleeing.
During his flight he burned his face with sulfuric acid in his possession, the statement added.
The suitcase fell on to the sidewalk of the hotel and briefly caught fire, but it was across the street from the historic synagogue, known as known as Shaar Hashamayim, or the Gate of Heaven. The hotel was not damaged and no one was injured in the attack.
Police initially said the man appeared to have panicked when he tossed the suitcase from the fourth floor. He later told his interrogators he was angered by the Israeli policies in the Palestinian territories.
The case held four containers of gasoline each attached to a glass bottle of sulfuric acid meant to shatter on impact and ignite the makeshift bomb. It also contained clothes, cotton strips, matches and a lighter.
Authorities described the suspect as an addict, who was repeatedly jailed for dealing and abusing drugs as recently as 2007. He also spent time in a rehabilitation center and was jailed in Libya for using forged documents.
The man was implicated in attacks organized in the 1980s by Islamic militant groups targeting video stores. He was not charged in any of these incidents however.
Egypt's once thriving Jewish community largely left the country 50 years ago during hostilities between Egypt and Israel, but a number of heavily guarded synagogues, open only to Jews, remain.
The downtown synagogue built in 1899 is Egypt's largest.
It is the only one still conducting services for the Jewish holidays, which are sometimes attended by Israeli diplomats.
