But the officials, citing initial testimony of the girlfriend, said the men told the couple they should not be together because they were not married and must immediately leave and go their separate ways. An argument followed and one of the three men stabbed Eid in the upper left thigh, near his genitals. He was hospitalized and died of his wounds a week later on Monday, according to the security officials who spoke on condition of anonymity because they were not authorized to talk to the media.
Suez is a stronghold of Islamists and voted overwhelmingly in support of Morsi in the June 16-17 presidential runoff against Ahmed Shafiq, a career air force officer and the last prime minister to serve under Hosni Mubarak before he was ousted in a popular uprising last year. Suez was a hotbed of the uprising.
The killing took place just one day after Morsi of the fundamentalist Muslim Brotherhood group was declared the winner of the runoff.
Last week, two musicians were murdered, also by suspected militants, in a Nile Delta province. Radical Muslims take a dim view of view music, considering it haram or prohibited, as a distraction from religious duties.
Such killings were very rare under the old Mubarak regime, which repressed the Muslim Brotherhood.
The security officials said there was no evidence to link the assailants in Suez to any of the main Islamic groups in Egypt. All these groups, including Morsi's Muslim Brotherhood, denied any link to the murders.
There have been a series of incidents across Egypt that point to radical Islamists to be seeking to bring the country more in alignment with Islamic rules since Mubarak's ouster. Several provincial universities are enforcing segregation between the sexes in classrooms and there have been incidents when militant students forced the cancellation of music concerts.
Hussein Eid, the victim's father, has said he would seek retribution for his son if the police don't catch the culprits. He did not accuse militants of murdering his son when he spoke to reporters on Tuesday after his son's funeral, which attracted about 3,000 mourners.
"My son's blood will not be wasted," said the father. Addressing Morsi, he said: "If you don't get me retribution, then my son's blood is on you."
Morsi, 60, has not mentioned implementing Islam's Shariah law a longtime goal of the 84-year-old Brotherhood since he narrowly defeated Shafiq. That was a departure from his hardline Islamic rhetoric in the run-up to the first round of voting in May, when the field of 13 candidates included several Islamists.
But some in Egypt suspect that Morsi, who belongs to a conservative wing of the Brotherhood, may be doing so deliberately to enlist the support of non-Islamist political groups in his battle of wills against the military generals who had taken over from Mubarak.
The generals have retained a great deal of authority after handing over power to Morsi on Saturday. They have given themselves legislative powers, a big say on drafting a new constitution as well as major foreign and domestic policy issues. They have also stripped Morsi of significant powers.
About a 100 activists, political parties and non-governmental groups have issued a statement calling on Morsi to protect women against what it said was growing incidents of harassment against women, particularly those not wearing the Muslim veil.
"These incidents don't constitute just assaults on women, but on the entire Egyptian society that has over many centuries been characterized by intellectual and cultural diversity," said the statement. "They require swift measures from the relevant state institutions and the president that guarantee the protection and safeguarding of women's dignity and the security and safety of the whole society."