Tsvangirai, a former trade union leader, defeated Mugabe in a first round of voting on March 29, but not by enough to secure an outright victory.
He had been abroad lobbying regional leaders to pressure Mugabe into holding elections under the watchful eye of regional peacekeepers and election observers.
Both the MDC and Zanu-PF were scheduled to hold rallies on Sunday.
The aftermath of the disputed first-round polls, the results of which were delayed by nearly five weeks, has been marked by violence that the opposition claims is designed to rig the run-off.
On his return on Saturday, Tsvangirai made clear his position on several lingering questions.
Firstly, he rejected the idea of a coalition government with Mugabe, which some have suggested would allow the 84-year-old leader a graceful exit and prevent further violence.
He also called for regional peacekeepers and election monitors from regional body, the Southern African Development Community (SADC), to be deployed by June 1.
"I am hoping that on Tuesday when they [SADC] meet they will be able to concretise but I told them by the 1st of June you should put these people on the ground otherwise we don't need them," he said.
No Western monitors were allowed to oversee the first ballot and teams from SADC and the African Union were widely criticised for giving it a largely clean chit.
Tsvangirai is threatened by a treason charge after he was accused of plotting to overthrow Mugabe with connivance from former colonial power Britain in April.