On Friday, Botswana - the African country to take the toughest stance against Mr Mugabe - urged Zimbabwe's neighbours not to recognise the election result.
The comments came as the opposition Movement for Democratic Change (MDC) accused the government of trying to wipe out the parliamentary majority that it won in March.
The party holds a majority of 10 seats in the 210-seat parliament.
But at least 10 of its newly elected MPs are either in prison or wanted by the police on a range of charges, the BBC's Peter Greste reports from Johannesburg.
Zimbabwe's state-run Herald newspaper reported that one MP was wanted for provoking political violence and he is now on the run.
The MDC said another of its MPs had been abducted, while 53 are fighting court challenges to their electoral victories.
Hero's welcome
Mr Mugabe spoke on Friday on his return to Zimbabwe from an African Union summit in Egypt, where African leaders called for a unity government.
Supporters were ferried to the airport to greet Mr Mugabe on Friday
But he said that the votes of those who supported him in the run-off "can never be rejected by anyone".
"We will reject that rejection ourselves, we will never accept it. And that is what I told the African Union."
He also said that MDC leader Morgan Tsvangirai and his supporters "must disabuse themselves of their claim (to power)".
"We are open to dialogue but reality is reality and it has to be accepted... I am the president of the Republic of Zimbabwe."
Mr Mugabe's movements since the summit have not been reported.
Zimbabwean journalist Brian Hungwe said ruling party Zanu-PF youths mobilised people in the townships around the capital, Harare, to go to the airport to welcome Mr Mugabe home.
The crowd danced and sang election campaign anthems - some held placards saying "No to dialogue".
Meanwhile, military police have been seen forcibly closing down ruling party bases in townships used to intimidate people ahead of last week's election.
It has come as a shock to many township residents to see the security forces turning against Zanu-PF supporters, beating them up and telling them to shut their bases, Brian Hungwe says.
It is thought that now that the elections are over, the party wants to get rid of the unpopular bases and disband the militia, he reports.
Continuing violence
On Wednesday, Mr Tsvangirai said the violence had to end before talks on sharing power could be entertained.
People at the US embassy say they were displaced in election violence
The MDC said on Friday that 103 of its supporters had been murdered in continuing post-poll intimidation and 1,500 party activists were in police custody.
"About 5,000 of our supporters, mainly polling agents and council candidates, are still missing after having been abducted by Zanu-PF militia and state security agents in unmarked vehicles," the MDC's Nelson Chamisa said in a statement, AFP news agency reports.
Botswana's Foreign Minister Phandu Sekelemani said Zimbabwe should not be able to take part in meetings of the Southern African Development Community (Sadc) "until such time that they demonstrate their commitment to strictly adhere to the organisation's principles".
But Mr Mugabe appeared to rebuff such African criticism.
"If there are some who may want to fight us, they should think twice," he said.
"We don't intend to fight any neighbours. We are a peaceful country, but if there is a... neighbouring country that is itching for a fight, then let them try it."
He also dismissed any threats from British companies to stop doing business with Zimbabwe.
"The British are threatening to withdraw their companies. We say the sooner you do it, the better," Mr Mugabe said, raising cheers from the crowd.
The European Union said on Friday that it would only accept a result that respected Zimbabwe's first round on 29 March, when official results gave Mr Tsvangirai more votes than Mr Mugabe - but not enough to avoid a run-off.
A statement from the EU's French presidency said any settlement should be followed by a brief transition period, then fresh elections.
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