Crowds filled city centre streets as moves to force the veteran leader to stand down gathered pace.
Many of the demonstrators were waving national flags and singing and dancing in an outpouring of elation at the expected fall of the 93-year-old despot.
Marcher Fred Mubay said: “It’s like Christmas. We have been suffering for a long time and now we are finally happy.”
Frank Mutsindikwa, 34, said: ”These are tears of joy. I’ve been waiting all my life for this day. Free at last. We are free at last.”
The military said it “fully supported” the “solidarity march” after being “approached by several private volunteer organisations seeking to freely move and express their desires”.
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The army seized power four days ago but Mr Mugabe has so far refused to bow down to demands to leave office.
Senior officers and ruling Zanu-PF party leaders now appear set on forcing Mr Mugabe out within the next 48 hours.
A senior member of ZANU-PF earlier said: “If he becomes stubborn, we will arrange for him to be fired on Sunday.
“When that is done, it’s impeachment on Tuesday.”
The Herald newspaper reported ZANU-PF would convene a special Central Committee meeting on Sunday to “realign the revolutionary party with current political developments”.
The army wants Mr Mugabe to leave office quietly and allow a transition government to be formed under Emmerson Mnangagwa, whose sacking last week as vice president sparked the army action.
But the generals want to make sure Mr Mugabe cannot hand the leadership to his wife, Grace, 41 years his junior, who appeared on the cusp of power after Mr Mnangagwa was pushed out.
The “grand old man of African politics” appears to be running out of options with the army camped on his doorstep, Mrs Mugabe under house arrest and key political allies in military custody.
Police have shown no resistance to the coup and Chris Mutsvangwa, the leader of Zimbabwe’s influential war veterans, said Mr Mugabe would not be allowed to resist the military and remain in power.
Mr Mugabe, in power since securing indepence from Britain in 1980, is still revered by some as an elder statesman and heroic freedom fighter.
But he is reviled by critics both at home and abroad who accuse him of violence, vote-rigging and corruption and of wrecking a once-prosperous economy.