In the capital of Harare, Mugabe spoke at Heroes' Day, an annual celebration when Zimbabwe honors those who were killed during the country's fight for independence in the 1970s, the BBC reported.
The Movement for Democratic Change of Mugabe's chief rival, Prime Minister Morgan Tsvangirai, boycotted the event and has challenged the results of what it called a "stolen election." It also demanded that the election be rerun.
In a statement Monday, Tsvangirai urged calm, saying Zimbabwe wasn't having a national celebration but was "a nation in mourning."
"We must all remain calm as we celebrate Heroes' Day," he said in the statement. "I know that we will always be a heroic people."
Mugabe won 61 percent of the vote in the election on 31 July, while Tsvangirai claimed 35 percent, official results indicated.
Mugabe's Zanu-PF party also picked up a parliamentary majority of more than two-thirds in the election, winning 160 of the 210 seats.
The MDC charged massive voter fraud on Election Day by Zanu-PF, even though monitors said they saw relatively few irregularities, the BBC reported.
The MDC said it has "strong evidence of electoral irregularities," including bribery, "assisted voting" abuse and voter roll manipulation. It said about a million voters in urban areas -- Tsvangirai strongholds -- were turned away.
Mugabe, 89, hasn't been sworn in to his seventh consecutive term because of the appeal.
The nine-member Constitutional Court is expected to take up the MDC's complaint this week. It has up to two weeks to deliver a decision.