El-Sisi's made the call at a Ramadan Iftar attended by representatives of most of the country's political forces, business associations, ministers, leading MPs and senators, opposition figures, media people, journalists and youth leaders.
El-Sisi said that recommendations for this dialogue will be referred to the House and Senate for further discussion.
Egyptian MPs agreed that the outlawed Muslim Brotherhood cannot be invited to any expected political dialogue.
MP Mahmoud Badr said in a statement that he believes that President El-Sisi's call for a political dialogue is directed to civilian forces only.
"Those who have blood on their hands or were implicated in terror-related crimes cannot be invited to such a national political dialogue," said Badr, adding that "the Muslim Brotherhood was designated a terrorist organisation in 2013, and so nobody can expect that members of such a terrorist organisation can be invited to such national dialogues."
Badr said that during the iftar ceremony, President El-Sisi referred to the TV series El-Ikhtiar 3, which documents the years of confrontation between the Muslim Brotherhood and civilian forces.
"According to the president during the Iftar ceremony, El-Ikhtiar 3 is showing exactly what happened on the ground in Egypt between 2012 and 2013," said Badr, adding that "these words clearly mean that the Muslim Brotherhood is a terrorist organisation and can't be part of any national dialogue."
In his statement before the Iftar ceremony on Tuesday evening, President El-Sisi said Egypt lost $38 billion in its war against terrorist organisations after the year 2011.
Badr also indicated that President El-Sisi's support for releasing activists does not apply to the Muslim Brotherhood.
"This applies to civilian activists and not to members of terrorist organisations with blood on their hands," said Badr.
On 24 April, the prosecutor-general announced a decision to release 41 pretrial detainees, mostly lawyers, human rights activists and journalists. President El-Sisi said on Tuesday that he was happy that they had been released, noting that “the homeland should be wide open for all and differences of opinion should not harm the nation.”
Moushira Khattab, president of the National Council for Human Rights, indicated that most of the released detainees were political activists or journalists.
“We are hopeful that others who are not involved in terror-related cases will be released,” she said.
Most of the 41 released detainees were in custody pending trial in political or freedom of speech cases.
Tarek Radwan, chairman of the House of Representatives’ Human Rights Committee, said in a statement that the release of activists and journalists would help pave the way for a successful political dialogue.
"Those released are civilian activists and not members of terrorist organisations," said Radwan, also agreeing that "the Muslim Brotherhood can't be invited to any proposed national dialogue."
In a statement issued on Wednesday, the leftist Tagammu Party said it strongly supports El-Sisi's call for a political dialogue as it reflects a national need.
"But this dialogue should be confined to civilian forces only, including recognised political parties and civil society organisations, with the objective of drawing up a new political roadmap for the coming years," said El-Tagammu's statement.
MP Faridi El-Biaddi, a member of the leftist Egyptian Socialist Democratic Party, also said in a statement on Wednesday that El-Sisi's call for political dialogue is directed to all civilian political and social forces.
“We saw symbols of some of these forces attending the iftar ceremony and I think they are the only ones who will be invited to the proposed dialogue,” said El-Biaddi.
El-Biaddi also agreed that civilian activists serving prison sentences or are in custody pending trial are the ones expected to be released in the future.
"But we do not expect that members of terrorist-designated organisations who were implicated in terror-related crimes will be released," said El-Biaddi, concluding that "we want a nation for all – Muslims and Christians, majority and opposition – but not for radical and terrorist forces."
Former MP Kamal Ahmed also warned in a press interview on Wednesday against inviting the Muslim Brotherhood to the proposed political dialogue.
"Inviting this organisation to such a dialogue means that they could be integrated into the political process again and this will be quite a dangerous development," said Ahmed, wondering "how, while we are watching the anti-Brotherhood TV serial El-Ikhtiar, can we open the door for this terrorist organisation to come back to political life?"
Ahmed, a founder of the Arab Nasserist Party, said "the call for a national political dialogue should not be directed only to gather support from political forces for a new loan deal with the IMF or satisfy the American who are openly exerting political pressure on Egypt."
Independent MP Mostafa Bakri also tweeted on Wednesday that he has high hopes that "the call for a wide-ranging dialogue will put an end to the state of political sclerosis in Egypt."
Bakri also agreed that the call for political dialogue should be directed to all civilian forces without exception.
"The only exception is forces which mix religion with politics or use violence to achieve their ends like the Muslim Brotherhood," said Bakri.