"This is a historic moment for SADC and a defining moment for Africa," Tsvangirai said in a statement issued by the MDC in Johannesburg.
"We can show the world that we, Africa, can solve our own problems and safeguard democracy and the rule of law.
"He [Mugabe] should recognise that he has lost and let me get on with making our great country great once more."
Tsvangirai said the delay, which has sparked an international outcry and tensions inside Zimbabwe, had wasted precious time in turning around a country dealing with inflation at more than 150,000 per cent and massive food shortages.
Mugabe had initially been going to attend the summit.
The extraordinary summit was called by Levy Mwanawasa, the Zambian president, to discuss the delays in the release of Zimbabwe's presidential election results that have left the country in limbo.
Thirteen days have passed since the election in which Mugabe's Zanu-PF suffered a major blow, losing control of parliament, with no word on who won the presidency.
A senior official in Zimbabwe's foreign affairs department said the emergency meeting was unnecessary and that the electoral commission was busy collating results.
"We believe this meeting really is not necessary because Zimbabwe has made it quite clear that they are going to announce the results [of the presidential election]," state television quoted Joey Bimha, foreign affairs permanent secretary, as saying.
|Tsvangirai is attending the emergency|
SADC meeting in the Zambian capital [AFP]
Bimha said Zimbabwe would be represented at the summit by himself; Emmerson Mnangagwa, the housing minister; Patrick Chinamasa, the justice minister; and Simbarashe Mumbengegwi, the foreign minister.
Al Jazeera's Kalay Maistry, reporting from Lusaka, said that there was unlikely to be much "tough talk" on Zimbabwe at the summit.
"SADC is pretty much split, with one pro-Mugabe camp and one almost anti-Mugabe. Countries like Tanzania and the new president in Botswana [Seretse Khama Ian Khama] are likely to be critical [of Mugabe]," Maistry said.
"People and observers here are simply saying the spirit and purpose of the summit has already been killed by the fact Mugabe has decided not to be here. But on the other hand it will be an opportunity for members of SADC to get the other perspective - Morgan Tsvangirai will be here and he will get an opportunity to make a presentation."
The MDC, in results it collated from figures posted outside 9,000 polling stations, has said Tsvangirai is the outright winner of the elections, while the Zanu-PF has called for a run-off with Mugabe as its candidate.
The MDC on Thursday ruled out Tsvangirai's participation in any second-round vote, accusing Mugabe of having launched a campaign of intimidation that would effect the outcome.
On Friday, the party called for a general strike to force the official announcement of the results, issuing pamphlets that requested Zimbabweans to stay home.
The MDC also plans a rally for Sunday, though police have announced a ban on rallies in Harare, the Zimbabwean capital.