The demonstrators urged the government to prepare the ground for early elections after Morsi relinquished power, Egyptian media reported.
The protest gathering was called by a number of opposition groups, including the Al-Dustur party of former UN atomic watchdog chief Mohamed ElBaradei and the April 6 movement which spearheaded the 2011 uprising to oust then president Hosni Mubarak.
Marches originated in various parts of the capital and were to converge on Tahrir Square, which was the focal point of the anti-Mubarak uprising.
At the head of one march people were carrying two large banners, one reading "an early presidential election" and the other "a unifying constitution for Egypt."
Marchers from the Tamarod (rebellion) campaign, which claims to have garnered more than two million signatures demanding that Morsi resign, collected more names from people along the route.
State media said security had been beefed up around the interior ministry, close to Tahrir Square, as it has been the scene of violent confrontations in the past.
The opposition accuses Morsi of governing only in the interests of his Muslim Brotherhood, while he insists he is the "president of all Egyptians."
Since Morsi was elected last June, Egypt has continued to suffer from a serious political and economic crisis, and there have often been frequent clashes, sometimes deadly, between his opponents and supporters.