The Egyptian Interior Ministry identified the attacker as Mahmoud Salah-Eddin Abdel-Raziq and said he suffered from "psychological disturbances".
Earlier, police said three men had been arrested in four simultaneous church assaults, one of them foiled by police. They said 17 people were wounded, and one later died.
The discrepancies between the reports could not be immediately explained. However, the government has always tried to downplay incidents that can be perceived as sectarian in nature so as not to inflame tensions between the Coptic minority and Muslim majority.
"This morning a citizen attacked three worshippers inside the Mar Girgis church in al-Hadhra with a knife and then fled and went into the Saints church, where he attacked three other worshippers and again fled," the ministry statement said. "While he was trying to enter into another church, he was arrested by police."
The statement said one of the worshippers died from his wounds. The semi-official Middle East News Agency identified the victim as Nushi Atta Girgis, 78.
Alexandria police earlier said they had arrested three men in the attacks. One was said to have attacked two churches; one attacked a third church; and the other was arrested during a foiled attack on a fourth church.
Hundreds of angry Copts gathered in front of the churches to protest against the attacks, and witnesses said clashes erupted between Christians and Muslims in the Sidi Bishr suburb, near Saints church.
Father Augustinos, who heads the Mar Girgis church, said: "We are trying to calm the situation after many of our youth started protesting. It doesn't do any good for the country to make protests."
Abdullah Osman, an official with the ruling National Democratic Party, told the Associated Press: "They went to the churches to explain that the attackers are insane and that the people should not blow things [out of proportion]."
Coptic Christians account for about 10 per cent of Egypt's population of 72 million. Egypt's last sectarian clashes were in Alexandria last October, when Muslims attacked churches and shops over the distribution of a DVD of a play deemed offensive to their religion.Reuse content