A Morsi loyalist was killed in Tanta in the Gharbiya govenorate in the Nile Delta, Ahram Online reported.
In Mansoura, in the same region, hundreds of residents attacked a pro-Morsi march and police fired tear gas.
Similar clashes occurred in the Nile Delta's Sharqiya govenorate, with pro- and anti-Morsi crowds throwing stones at each other.
Cairo witnessed about 10 marches through its streets.
Thursday night, the U.S. Embassy in Cairo issued warnings to Americans of possible violence
The National Alliance to Support Legitimacy, an Islamist coalition, called the protests the "Friday of Martyrs" and called for nationwide demonstration. It said it planned 28 in Cairo alone on Friday.
Despite the exhortation, the turnout was the lowest for Friday marches since the end of June. The number of protesters has fallen following the arrests of several Muslim Brotherhood leaders during the past week. The most significant arrest was that of Mohamed Badie, the Muslim Brotherhood's Supreme Guide.
The army and police were sprinkled throughout the vicinity of a Nasr City mosque where pro-Morsi supporters held a sit-in for six weeks. Security forces have also been increased at the defense ministry and the presidential palace, and all entrances to Tahrir Square have been closed.
The violence erupted as a conservative Islamist, moderate Islamist and leftist secular party cautiously welcomed a plan by Egypt's deputy prime minister to end the political crisis.
The peace plan from Ziad Bahaa el-Din, a lawyer and a former head of Egypt's investment authority, explicitly rejects violence and respects places of worship and freedom of religion, but does not explicitly seek to reintegrate the Muslim Brotherhood into Egypt's political process, el-Din told Egypt's CBC-TV.
The initiative, presented to the interim Egyptian Cabinet Wednesday, calls for inclusion of and non-discrimination against all political and ideological groups, provided they abide by the law.
It insists on moving forward with Egypt's political "road map," or "constitutional declaration" by military-appointed President Adly Mansour.
The road map calls for amending or replacing the current Islamist-backed Constitution, adopted in 2012. It also envisages parliamentary and presidential elections early next year.
El-Din's initiative also demands an end to the state of emergency imposed by Mansour a week ago, state newspaper al-Ahram reported.
Another point calls for freedom of the press, speech and assembly, including the right of peaceful protests and strikes, but also gives security forces the right to take lawful and restrained action against protesters who are not peaceful, block highways or threaten people's livelihoods.
The Nour Party of Islam's ultraconservative Salafi sect, expressed cautious optimism about the proposal, especially since it seeks to end the state of emergency, and asked for a meeting with el-Din to discuss it, party spokesman Sherif Taha said.
The party, which seeks to implement strict Sharia law, called on the pro-Brotherhood Anti-Coup Alliance to consider the proposal as an option to ending the crisis, al-Ahram reported.
The alliance had no immediate comment.
The Brotherhood and its Freedom and Justice Party also had no immediate comment.
The 13-month-old Strong Egypt party, started by former Brotherhood member and presidential candidate Abdel Moneim Aboul Fotouh, said it considered el-Din's plan a good starting point for national reconciliation.
"Still, this depends on serious mechanisms to adopt the freedoms and rights mentioned in the initiative, including independent investigations in the massacres that happened in Sinai, Republican Guards Club, the dispersal of pro-Morsi sit-ins, the torching of churches, the attacks on police stations, the killing of protesters and sectarian violence," said a statement from the party, which considers itself economically and socially moderate.
The leftist Popular Alliance Party said it supported the initiative and called on the Cabinet to adopt it, al-Ahram said.
"Any attempt to confiscate public freedoms will create a growing environment for violence and terrorism," the party said in a statement.
"Fighting terrorism does not need exceptional laws as much it needs a complete vision like the one presented by the vice prime minister's initiative that ensures social justice," the statement said.
The protests came a day after former autocratic President Hosni Mubarak -- overthrown in a 2011 pro-democracy uprising -- was freed from jail while Morsi, his freely elected successor, remained under indefinite detention in an undisclosed location with no access to legal counsel.
About 1,000 civilians have been killed since security forces broke up two pro-Morsi sit-ins in Cairo last week.