Tsvangirai, a former trade union stalwart and leader of the Movement for Democratic Change (MDC), pulled out of an election run-off in 2008 following a flare-up in violence which claimed at least 200 opposition supporters.
Mr Tsvangirai, who was battling cancer, died on February 15.
Zimbabwe's President Emmerson Mnangagwa has been speaking to BBC Minute's Seren Jones in the capital Harare.
Mnangagwa has repeatedly promised fair elections as he seeks to attract foreign investment after years of global sanctions over alleged human rights abuses.
Tsvangirai's death came as tensions over his succession are threatening to tear apart the MDC, which he had led since its formation in 1999.
His death leaves Zimbabwe's opposition in disarray with the first post-Mugabe elections approaching.
Mnangagwa told journalists that Tsvangirai wanted to ensure that Zimbabwe was a democratic state.
Acting MDC-T president Nelson Chamisa said the party will work hard to win in the upcoming vote as a way to honor Tsvangirai. "Comrades, you are allowing power to get in the way of reason and dignity", tweeted Alex Magaisa, a law lecturer at Kent University in Britain and former adviser to Tsvangirai.
In the end, the opposition leader made the same mistake that Mugabe did, political analyst Alexander Rusero said: Even as his health deteriorated Tsvangirai failed to "anoint" a successor. "We will always remember him".