Rejecting PM Morgan Tsvangirai’s claims that the vote was stolen, he said those against him could “go hang”.
Morgan Tsvangirai’s Movement for Democratic Change (MDC) boycotted the speech.
The MDC has lodged a legal challenge against the result of the “stolen election”, demanding it be rerun.
Robert Mugabe won 61% of the vote in the election on 31 July, while Morgan Tsvangirai came second with 35% and Welshman Ncube third with 3%, according to official results.
The president’s Zanu-PF party also gained a parliamentary majority of more than two-thirds, winning 160 of the 210 seats.
In his Heroes’ Day speech, which dealt with a series of national issues, Robert Mugabe focused at one point on his election victory and called for celebrations.
“Those who lost elections may commit suicide if they so wish. Even if they die, dogs will not sniff their corpses,” he said.
“We are delivering democracy on a platter. We say take it or leave it, but the people have delivered democracy.”
Zimbabwe’s Western detractors had been “put to shame”, he added. “Never will we go back on our victory.”
Non-governmental organizations had been used to rig elections in 2008, he claimed, but Zanu-PF had never stopped planning since then and had “buried thieves in our midst”.
“We found we were dining with and sharing our bed with thieves. We will never give thieves the power to rule.”
Robert Mugabe’s main rival Morgan Tsvangirai won the first round of the 2008 presidential vote, but official results said he had failed to win outright.
He later pulled out of the second round because of attacks on his supporters, and eventually a power-sharing agreement was worked out.
Heroes’ Day is Zimbabwe’s proud annual celebration, when the country remembers those who died during the 1970s fight for independence.
Robert Mugabe was speaking at National Heroes’ Acre, the monument in the capital where some of those killed are buried.
Morgan Tsvangirai earlier called for calm, saying there was no national celebration for the day but rather “a nation in mourning”.
In a statement, published by the NewsDay newspaper, Morgan Tsvangirai said the majority of Zimbabweans were “still shocked at the brazen manner in which their vote was stolen”.
“We must all remain calm as we celebrate Heroes’ Day. I know that we will always be a heroic people.”
The MDC’s boycott of the national commemoration has exposed the deep rifts at the heart of this troubled country, our correspondent says.
Robert Mugabe has not yet been sworn in for a seventh consecutive term, since the appeal is ongoing. He maintains that he and Zanu-PF won free and fair elections.
The MDC has said it has “strong evidence of electoral irregularities”, including bribery, abuse of “assisted voting”, and manipulation of the electoral roll.
African and regional monitors praised the poll for being peaceful but noted some irregularities.
But a local observer group, the Zimbabwe Election Support Network (Zesn) and its network of 7,000 observers, said that about one million voters – mainly in urban areas – were “systematically disenfranchised” by being omitted from the voters’ roll or turned away.
The nine-member Constitutional Court is expected to discuss the complaint this week. It has up to two weeks to deliver its verdict.
But with several judges being supporters of Robert Mugabe, few expect the MDC challenge to bear fruit.
In a separate development on Sunday, state radio reported that the ministry of mines had denied a report in the Times newspaper that it had agreed to sell Iran uranium for its nuclear programme.
A ministry statement was quoted as stressing that the report was “a malicious and blatant lie”, and that no export licenses had been issued.
Iran’s foreign minister has also denied the report.
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