Security officials reported clashes outside some churches in the country's second largest city but they stopped short of spilling over in to the violence that left one person dead and 21 wounded on Satuday.
Mustafa Meshaal, who was wounded during the clashes between Muslims and the Christian Coptic minority, died of his wounds in hospital.
The violence erupted after an attack on Coptic worshippers in three churches in Alexandria.
Security sources said 45 people had been arrested following the violence that flared after the funeral for 78-year-old Meshaal.
The interior ministry said it had arrested the suspected assailant, 25-year-old man named Mahmud Salaheddin Abdul Razek.
A spokesman described him as "mentally unstable", a claim which sparked anger among the Coptic community.
The Egyptian Coptic church has blamed a "terrorist plot" for attacks on the three churches and rejected government claims that they were the work of one "mentally unstable" man.
Meanwhile edgy Christian worshippers on Palm Sunday asked strangers wishing to enter churches to flash their identity cards and checked their wrists for a tattoo of the cross.
Security sources said scuffles broke out outside the Al-Quidissin church following prayers marking Palm Sunday.
But the leaders of both communities appealed for calm and no major incidents were reported.
Pro-democracy protest
Meanwhile, a group of about 40 human rights and pro-democracy activists gathered in front of the prosecutor general's office in Cairo on Sunday to denounce the Alexandria attacks and demand justice.
George Ishaq, a leader of the pro-reform Kefaya (Enough) movement, blamed the government and the police forces for failing to prevent attacks on churches and warned of an escalation in sectarian violence.
"The continuation of the situation as it is could ignite a fire that will consume us all," he said.
The activists also carried placards criticising the government. "Who will bring to account the instigators of sectarian strife?" read one of them. "Job opening: Mentally deranged person wanted to cooperate with the interior ministry," read another.
The Egyptian parliament condemned the church attacks and announced it was forming a committee to investigate the incident.
It came as prosecutors renewed for 45 days the detention of Abdul Razek, whom judicial sources said would be placed under observation to determine his mental health.
Following the incident, the interior ministry said the rampage was carried out by a single attacker within the span of an hour, revising an earlier account by police officials who claimed three people had been involved.
Friday's attacks were the most serious incidents of sectarian violence since a protest by Muslims accusing an Alexandria church of hosting a play offensive to Islam left three dead in October.
Egypt's Copts, the largest Christian community in the Middle East, account for an estimated 10 percent of the country's 73 million inhabitants and complain of systematic discrimination and harassment. They will mark Easter on April 23.