An Egyptian army vehicle fired live rounds in the direction of Brotherhood supporters who had been pushed back by security forces when they tried to enter Cairo's Tahrir Square, the symbolic heart of the 2011 uprising.
Four Brotherhood supporters died in clashes in two Cairo districts.
Major General Sayed Shafiq, assistant interior minister for public security, denied any protesters had died in the southern city of Assiut. Medical and health sources had earlier said four people had been killed in Assiut, without saying which side they were on.
In Cairo, onlookers threw rocks at pro-Mursi protesters, who hurled them back. Riot police earlier fired tear gas to push back the march.
Thousands of protesters headed toward the site in northeast Cairo of one of the former Brotherhood protest camps crushed by security forces in August. By late afternoon, protesters had retreated from the area.
Members of the Brotherhood, which is banned by court order, tried to reach the presidential palace but were turned back by police.
But the state news agency claimed protesters failed to reach the defence ministry and a Republican Guard facility. There was fighting in Alexandria and two Nile Delta cities.