The Egyptian government in its initial response has ordered military special forces to assist the police in securing vital state facilities across the country.
Israel offered condolences to the families of the victims of two bombing attacks on churches in Egypt and called for a worldwide fight against terrorism.
Trump had earlier expressed his support for Egypt and El-Sisi through his official Twitter account.
"Hamas wishes safety, security, stability and prosperity for Egypt and its people", Barhoum added.
Attacks in the Sinai, including the murder of a Copt in the city of El Arish whose house was also torched, prompted some Coptic families to flee. The Pope has expressed condolences for those killed in the bombings. Authorities said the Coptic pope for Alexandria, Pope Tawadros II, was inside leading the prayers but was not injured.
The US Embassy in Egypt condemned "the heinous, reprehensible terrorist attack against peaceful worshippers".
Israel shut its Taba border crossing to Egypt after its anti-terrorism office warned of an "imminent" attack there.
Copts, who make up about 10% of Egypt's 91 million residents, have been the target of increased persecution and discrimination since the toppling of Hosni Mubarak's regime in 2011.
"The Alexandria bombing targeted the head of the [Coptic Orthodox] church himself", he noted. The group has threatened further attacks. Downtown is usually busy but was relatively quiet on Sunday because of the holiday. But Copts in Tanta said security was nearly non-existent on Sunday despite repeated warnings in recent weeks.
Given such incompetence, denial or collusion by Egyptian authorities, Coptic Solidarity demands an independent inquiry by the United Nations to evaluate the Copts' situation and to recommend necessary measures to alleviate their dire situation and to avoid repetition of the tragic situation of Christians in Iraq and Syria. "It is failing to bear its security responsibilities".
Another suicide attack killed at least 28 people inside St George's Church in the Nile Delta city of Tanta.
For a community already suffering from an attack which killed 30 at a church connected to the main Coptic Christian cathedral in Cairo in December 2016, Sunday's attacks have given rise to even greater concern over the security in Egypt.
The move by Mr. Sisi is likely to raise concerns among human rights activists, observers say, the president, who is a former army chief, has been criticized by local and worldwide groups for severe restrictions on civil and political rights in Egypt.
Egyptian blogger Maged Butter told CNN he saw five or six ambulances and blood stains 100 meters away from the site of the explosion - which happened near the church gate.