Morgan Tsvangirai, the MDC leader, says that he won an outright victory in the first round of voting two weeks ago.
Robert Mugabe, the incumbent president, has instead been preparing for a second round run-off.
Wayne Bvudzijena, a police spokesman, said on Friday: "We see no reason for rallies since we have had elections."
Nelson Chamisa, MDC spokesman, said that the party had planned a rally for Sunday.
"You can't be a political organisation and not hold a rally, that is what makes us who we are, how we communicate with our supporters," he said.
"We cannot accept a declaration of a police state. People have just voted for change, for democracy and what do they get? This is unacceptable. This is ridiculous."
The ruling party and Mugabe "are also eagerly waiting for the [election commission] to complete its ballot votes verification freely without any interference and without pressure not to release the results," he said in a statement, according to the state-run Herald newspaper.
Meanwhile, state radio reported that Mugabe would not attend a summit of southern African leaders in Zambia, concerning the politicial deadlock in Zimbabwe.
Zimbabwe would instead be represented at the Southern African Development Community (SADC) summit by four senior ministers, the report said.
Tsvangirai, whose attendance at Saturday's summit in Lusaka has already been confirmed, met Thabo Mbeki, South Africa's president, on Thursday, officials said.
Mbeki has come under fire for failing to condemn the long delay in announcing the presidential poll result.
"The meeting went well. The details of it are not at this stage for public consumption," Nqobizitha Mlilo, an MDC spokesman, said.