The Constitutional Court has 14 days from the day the presidential challenge is lodged to render a decision.
"We will rest when this country is liberated", Jameson Timba, the MDC's chief election agent, told journalists standing outside.
Chamisa's lawyer Thabani Mpofu said he had asked the Constitutional Court to nullify the July 30 vote and that his court application meant Mnangagwa's swearing-in had been halted. We have a good case and cause!
European Union observers said that the ZANU-PF candidate had benefitted from an "un-level playing field" and some voter intimidation, though global monitors largely praised the conduct of the election. Elections are not won in court, they are won in the field.
But the delay to Mnangagwa's inauguration drew further attention to concerns over the election's credibility.
We are also deeply concerned that Zambia chose to hand over former Minister of Finance Tendai Biti to the Zimbabwean authorities, and in the face of a reported Zambian court order blocking his expulsion from Zambia.
"In the alternative, we seek that there be another election which complies with the dictates of the law", Mpofu said.More news: Argentina's Senate rejects bill to legalise abortion
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The aftermath of the polls has been marred by allegations by rights groups as well as by the MDC of a crackdown on opposition members, including beatings and arrests.
Mr Biti is the first senior opposition politician to be detained since Mr Mnangagwa took over from Mr Mugabe.
"Zimbabwe faces a awful threat from a group of people that has no respect for the law", Biti, who was granted bail Thursday, told the court before his case was adjourned until next week.
Earlier this month, Mnangagwa secured a comfortable victory, according to results from the Zimbabwe Electoral Commission, polling 2.46 million votes against 2.15 million for the 40-year-old Chamisa.
It said it had received numerous complaints of "hunting down" and intimidation, often by men in military uniform, of voters thought to have backed the opposition.
In the days following the poll, six opposition supporters died in clashes with the army, which has led some to question its neutrality.