Some Zanu PF supporters say a public protest staged by the MDC led by Morgan Tsvangirai was a waste of time.
They say it was an attempt by the MDC-T to revive its party, which performed dismally in the last general elections.
One of the top Zanu PF officials, Joseph Tshuma, told VOA Studio 7 the MDC-T should just forget about staging such public protests.
MDC-T spokesman, Obert Gutu, said Zanu PF should brace for more public protests.
Zanu PF party spokesman Simon Khaya Moyo told the state-run Herald newspaper that President Mugabe won his post democratically and said supporters of the opposition should vote him out of office rather than call for his resignation.
Moyo said if the people "still need him, they will vote for him again," in 2018, when Mugabe is expected to stand for re-election.
More than 2,000 supporters of the MDC-T party, led by Morgan Tsvangirai, marched in the streets of Harare, many of them wearing red in support of the opposition.
Police are often called to break up opposition rallies in Zimbabwe, and Thursday's march had originally been banned -- but a court overturned the police order on Wednesday.
Mr. Mugabe is one of Africa's longest-serving leaders, having been in power since 1980. Despite his age, he is still a compelling speaker and recently announced he will stand for election again in 2018.
Zimbabwe's past elections have been criticized by the United States and other powers as flawed, marred by violence and voter intimidation.
Opposition leader Tsvangirai and his movement say Mr. Mugabe's policies are responsible for Zimbabwe's long-running economic problems and food shortages.
Tsvangirai has lost the last three elections to President Mugabe, and has been charged in the past with plotting to topple the president.