But hardliners put paid to it, he said.
"The very same people who were coming to us for discussions organised the meeting and did not turn up for almost two hours, our guys left and we realised that the situation had totally changed, they were back to their plan," he said.
Earlier he said he had asked Zambian President Levy Mwanawasa, chairman of the Southern African Development Community (SADC), to launch a new initiative.
"President Mbeki needs to be relieved from his duty," Tsvangirai told a news conference in Johannesburg, adding that Mugabe had "unleashed an orgy of violence against the people" after the election.
Mbeki led a failed SADC mediation last year.
The MDC said hundreds of supporters had been seriously injured in attacks by ZANU-PF. The opposition says Mugabe is using militias to intimidate opposition supporters and help him rig victory in an expected run-off election against Tsvangirai.
Tsvangirai suggested there may need to be a special United Nations tribunal to judge crimes committed in Zimbabwe.
"I think the current wave of violence against the people must stop and the only way to stop (it) is that those who are committing those crimes must know that they must be answerable one day," he said.
POLICY SHIFT
In a policy shift, Mbeki's government called for the results to be issued rapidly and said it was concerned by the delay.
"When elections are held and results are not released two weeks after, it is obviously of great concern," government spokesman Themba Maseko said in Cape Town.
Mbeki had previously said the electoral process must take its course and there was no crisis after the elections.
His stance was seen as backing Mugabe over the delay.
Although ZANU-PF lost control of parliament for the first time, no results have been released from a presidential poll.
"The Zimbabweans need to be informed about those reasons for holding the results. But the most important thing is that the results need to be verified and released as soon as possible," Maseko said, briefing reporters on a Wednesday cabinet meeting.
