Abdullah, who had worked for an oil company, was linked to a "terrorist" network, a cell from which carried out a previous bombing of a Cairo church in December that killed 29 people, the ministry added in a statement.
Islamic State has waged a low-level war against soldiers and police in Egypt's Sinai Peninsula for years but it is increasingly targeting Christians and broadening its reach into Egypt's mainland.
The attacks in the Nile Delta cities of Tanta and Alexandria followed a Cairo church bombing in December and came weeks before a planned visit by Catholic Pope Francis meant to show support for Egypt's Christian minority.
The President of the Republic expressed his deepest condolences on behalf of the people and Government of the Saharawi Republic to President Abdel-Fattah Al-Sisi and the Egyptian people in this great loss, and solidarity and sympathy with the families of the victims.
The group later released a video threatening Egypt's Christians with more attacks.
President al-Sisi in a brief television appearance on Sunday had announced the state of emergency for three months.
"Worshippers, no matter what their belief is, should always be free to pray in peace", she stated.
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At least 44 people died, and more than 100 were injured, during bombings that targeted a Coptic cathedral and another Coptic church on an important holy day on the Christian calendar, Palm Sunday. A few hours later there was a second bombing in Alexandria, killing innocent men, women and children as they left a Palm Sunday Liturgy that was officiated by His Holiness Pope Tawadros II, Pope of Alexandria and Patriarch of the See of Saint Mark.
The former army chief met with U.S. President Donald Trump a week ago at the White House, seeking closer ties and discussing the fight against extremism.
Joe Stork of Human Rights Watch said el-Sissi "seems to think that more repression of all Egyptians is the simple answer to terrorist attacks".
"Wait for us, for we will wait for you", the group said in a statement. The majority in parliament backs Mr Sisi.
Approximately 10 percent of Egyptians are Christian, the largest minority in the Middle East.
More than 40 people were killed and dozens wounded in the bombings. The targets of the attack were St. George's church in Tanta and St. Mark's Cathedral in Alexandria. ISIS also claimed responsibility for that attack.