At least a dozen people were killed, and another 65 injured, in the latter attack.
ISIS later claimed responsibility for the planned attacks.
President Donald Trump also condemned the attacks and urged the Egyptian Government to handle the "unfortunate" incident properly.
The two Coptic churches appear to have been chosen for their symbolic value. A priest at St. George Coptic Orthodox Church served for years at one of the bombed churches.
The Coptic Pope Tawadros was leading the mass in Alexandria's Saint Mark's Cathedral when the bomb exploded.
The second struck outside Saint Mark's church in Alexandria, killing 17 people after a suicide bomber was prevented from entering the building.
El-Sissi called for the state of emergency, which parliament must approve first, after a meeting with his national security council on Sunday.
He also expressed confidence in el-Sisi's commitment to protect Christians and all Egyptians.
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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.
Egyptian Copts make up about 10 percent of the Muslim-majority country's 92 million residents. In December, an attack at a Coptic church in Cairo killed 25 people. Pope Francis will visit Egypt on 28-29 April. "This terrorist attack is devoid of all the principles of humanity and civilisation", it said in a statement.
President Abdel-Fattah al-Sissi announced a three-month state of emergency on Sunday. "Especially on Palm Sunday, a day when many people gather, more than any other time in the year".
Citing Health Minister Ahmed Emad, ON TV news channel reported at least 18 people, including police personnel, were killed and 41 injured in the suicide attack in Alexandria.
A source said Coptic Pope Tawadros II was inside the church when the bombing took place but he was not injured.
It may be recalled that yesterday's bombings were among the deadliest that were targeted at the minority Christian community in Egypt. "There was a clear lapse in security, which must be tightened from now on to save lives", he said.
The attacks on worshippers marking Palm Sunday in the Nile Delta cities of Tanta and Alexandria have been claimed by Islamic State.
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