President Abdel-Fattah el-Sissi called for a three-month state of emergency late on Sunday night and also sent elite troops across the country to protect key installations.
The Islamic State terror group claimed responsibility for the violence which became the single deadliest day for Christians in decades. It comes after a bombing at a Cairo church in December 2016 which killed 30 people.
Grand Sheikh Ahmed el-Tayeb, head of Egypt's Al-Azhar, the leading centre of learning in Sunni Islam, also condemned the attacks, calling them a "despicable terrorist bombing that targeted the lives of innocents".
The Health Ministry said six Muslims were among the dead in Alexandria.
The attacks in the northern cities of Tanta and Alexandria that injured 126 people came just weeks before Pope Francis is due to visit.
Pope Tawadros, the leader of the Coptic church who will meet Francis on April 28 and 29, was in the Alexandria cathedral at the time of the bombing but was unhurt, the Interior Ministry said.
The Coptic leader had held Palm Sunday services at the cathedral and the timing of the attack indicated the bomber had sought to assassinate him.
US president Donald Trump tweeted that he was "so sad to hear of the terrorist attack" against the American ally but added that he had "great confidence" that Mr el-Sissi "will handle the situation properly". The two leaders met at the White House on April 3.
Grand Sheikh Ahmed el-Tayeb, head of Egypt's Al-Azhar, the leading centre of learning in Sunni Islam, also condemned the attacks, calling them a "despicable terrorist bombing that targeted the lives of innocents".
Egypt has struggled to combat a wave of Islamic militancy since the 2013 military overthrow of elected Islamist president Mohammed Morsi.
His Grace Bishop Angaelos, General Bishop of the Coptic Orthodox Church in the United Kingdom, said after the massacres: "We pray for His Holiness Pope Tawadros II and all our Coptic clergy in Egypt who continue to serve their spiritual children faithfully and diligently at a time in which their leadership and pastoral care is needed by our whole community.
"We also pray for our Coptic Orthodox sisters and brothers who continue to be resilient in the face of ongoing and escalating attacks, and who resist the urge to react vengefully or reciprocally.
"We are also saddened by the news that members of the security services who attempted to foil the second bombing in Alexandria lost their lives in the line of duty. We pray comfort and resolve for their families and colleagues.
"As we continue into the Holy Week of our Saviour, we share in the pain and heartbreak of their families and of all those affected by today's incidents. As we celebrate the Feast of the glorious Resurrection at the end of this week, we are reminded that our life here on earth is a journey often filled with pain, at the end of which is a promised glorious and eternal life void of such suffering and evil."