The church, which stands at the site where Christians believe Jesus multiplied five loaves of bread and two fish to feed 5,000 of His followers, was damaged extensively in a fire earlier this month.
Sparked in an act of religious and racial hatred, the arson attack caused widespread condemnation in Israel as well as solidarity protests by non-Christian Israelis.
"This outrageous arson attack against the church is an attack on all of us," Israeli Prime Minister Netanyahu said.
Matthew Gould, the British ambassador to Israel, added that the attack is "a disgusting act of disrespect at one of Christianity's holiest sites."
Israel's security agency, the Shin Bet says the men responsible are followers of an "extremist Jewish ideology" that believes "only someone who fights Christianity can call himself a Jew."
Israeli's Yinon Reuveni, 20, from Ofakim, and Yehuda Asraf, 19, from Elad, face charges of aggravated arson, destruction of property motivated by hostility toward the public and conspiracy to commit a crime at the church.
The Roman Catholic Church is run by the Benedictine Order at Ein Sheva, next to Capernaum, on the northwestern shore of the Sea of Galilee.
Israeli security officials named two other suspects who have yet to be indicted as Mordechai Meir, 18, from Ma'aleh Adumim, and Moshe Urbach, 24, from Bnei Brak. The fifth suspect arrested in the case is an unnamed minor from Ramle.
Shin Bet sources say all of the suspects have been banned from Judea and Samaria in the past on suspicion of violent attacks on Palestinians or Palestinian-owned property.
The suspects were purportedly driven by a hateful anti-Christian ideology held by the so-called Hilltop Youth, a group of Jewish ultra-nationalists known for establishing illegal outposts in Judea and Samaria.
According to officials the incident happened on the night of June 17, where the suspects torched the church in order to cause harm to a Christian holy place.
The suspects allegedly drove to a gas station in west Jerusalem, where they filled up bottles with gasoline.
They then waited a few hours before allegedly making their way to a meeting room inside the church where they poured gasoline on the doors and walls and lit the fuel.
The group then spread gasoline on the door of the monks' living quarters, and poured a trail of gasoline to a yard outside, where they lit the fuel as well.
The arsonists then sprayed graffiti on a wall of the church labeling it as a place of idol worship.
During the blaze, the head of the church and a volunteer were treated for smoke inhalation by paramedics.
The building was almost completely gutted by the flames. Priests and volunteers say they expected a long, costly rebuilding process.
The Church of the Multiplication of the Loaves and Fishes was built in the 1980s, and sits on the site of fourth and fifth century shrines that are believed to commemorate the location of one of Jesus' most well-known miracles.
Matthias Carl Benedictina, one of the church's priests, noted that this was not the only attack against Christianity in the region.
He revealed that there have been over 50 acts of violence against Christian institutions by extremist groups in Israel in the past three years, sometimes targeting cemeteries and other Christian property.
The arson attack follows dozens of other suspected hate crimes committed against mosques and monasteries in Israel, the West Bank and East Jerusalem since 2009.