Police used tear gas to drive back protesters, some hurling rocks, who had blocked a main route in the capital Cairo.
Morsi was ousted on 3 July in what many have said was a military coup. The army says it was fulfilling the demands of the people after mass anti-Morsi protests.
Monday's battles erupted after hundreds of protesters, mostly members of Morsi's Muslim Brotherhood movement, blocked the Sixth of October bridge, a major route over the Nile and through the capital, and the nearby Ramses Square, a transport hub.
Police fired tear gas to try to break up the blockade. Protesters responded by throwing stones. Other clashes broke out in the Giza district, in the south-west.
The head of Egypt's emergency services, Mohamed Sultan, said two people had died on or around the bridge and five in Giza.
State media quoted health ministry official Khaled al-Khatib as saying 261 people were injured in the clashes, which lasted into the early hours of Tuesday. Khatib said 124 people were still in hospital.
Sultan said security personnel were among the casualties.
Members of the Brotherhood said security forces had used live ammunition, and accused them of attacking a peaceful protest.
"We were praying. Suddenly there was shouting. We looked up and the police were on the bridge firing tear gas down on us," protester Adel Asman told Reuters news agency.
State media later quoted officials as saying 401 people had been arrested for "provoking unrest".
SHI/SHI