The MDC insists that the run-off should be held on May 23, in line with laws which say the vote has to come within 21 days of the election results, which were announced on May 2.
The MDC also accuses the Zanu-PF of intimidating and attacking its supporters as part of efforts to rig the second-round vote, a charge the government denies.
Official results showed that Morgan Tsvangirai, the opposition leader, had beaten Mugabe in the election, but not by enough votes to avoid a run-off.
The parliamentary vote conducted on the same day, resulted in Zanu-PF losing its majority to the opposition for the first time since independence from Britain in 1980. The new parliament has not yet convened.
The MDC says at least 32 of its supporters have been killed by Mugabe followers since the first round took place on March 29.
There has been a steady rise in the levels of post-election violence which the United Nations warned this week could reach "crisis proportions".
Much of the violence has been in the countryside, a traditional stronghold for Mugabe but where he did worse than expected on March 29.
The MDC fears that voters will be too scared to cast their ballot in these areas, in the event of a lengthy delay.