The MDC appeared to be maintaining a slim lead over Mugabe's ruling Zanu-PF party in the official count of parliamentary elections, but the lack of official results has served to build the crisis.
Al Jazeera's Haru Mutasa, reporting from the opposition stronghold of Bulawayo, said some people believed the delay in the results meant the ruling party was rigging the elections and could stage demonstrations.
"Some people are saying the reason these results are taking so long is because maybe - they accuse - the government is trying to tamper with the vote," she said.
"A small group are saying that if it does happen they will maybe take to the streets. That's just a small group, most people here just want the results to come and go."
The electoral commission has said the delay is due to presidential and parliamentary elections being held at the same time and there being 60 constituencies more than in the last elections in 2005.
Mutasa said people were "not too concerned about the parliamentary results".
"They want to know who the president is going to be".
'Proceed with haste'
Tsvangirai called on Tuesday for the electoral authorities to "proceed with haste" but he has declined to declare himself the victor before the official results were released.
"The people of Zimbabwe have waited for this for so long and I think they can wait longer," he said.
"I am prepared to wait as long as the ZEC [the Zimbabwe Electoral Commission] confirms the results."
Tsvangirai dismissed speculation the MDC was negotiating with the Zanu-PF behind the scenes.
The AFP news agency reported quoting a senior Zanu-PF member that Mugabe had already agreed in principle to stand aside in favour of Tsvangirai, who Mugabe last month insisted would never be president in his lifetime.
Some rumours suggested the unprecedented hold-up is in order for Mugabe to negotiate a dignified departure from office.
But Bright Matonga, the deputy minister of information, dismissed the rumours of negotiations between MDC and Zanu-PF as part of "April fools day".
He said the delay in announcing the election results was down to logistical difficulties.
"You can understand why it is taking a long time," he told Al Jazeera.
"Before it was just one election - you were voting for the president and that was it - but this time your voting fro four people and 75 per cent of our voters come from remote areas."
Asked if Zanu-PF was ready for a run-off vote, Matonga said: "We are ready for all the options."
Meanwhile, Desmond Tutu, the former South African archbishop and Nobel laureate, has proposed in an interview with the BBC sending an international peacekeeping force to Zimbabwe in the wake of the unresolved elections.
He said he supported any deal that would stave off conflict in Zimbabwe.
Tutu said he believed the evidence supported claims by the MDC that it had unseated Mugabe.
Ban Ki-moon, the UN secretary-general, urged "utmost transparency" in the vote counting "so that the people of Zimbabwe can have full confidence in the process".
The US and Britain, Zimbabwe's former colonial ruler, have led international calls for Harare to respect the people's will and publish the election results.