"The time for national action is now," said Mr Tsvangirai, to enthusiastic cheers and applause, before adding: "What we would like to tell Mugabe is please go peacefully. If you don't want to go peacefully, we will remove you violently."
The head of Zimbabwe's main opposition party, the Movement for Democratic Change (MDC) has warned of potential violence if President Mugabe refuses to step down before elections scheduled for 2002.
Morgan Tsvangirai told a crowd of about 20,000 supporters that if Mr Mugabe refused to go peacefully, then he would be removed violently.
The opposition described their first anniversary rally as a victory celebration, not just marking their success in winning nearly half the contested seats in recent parliamentary elections, but also in anticipation of the departure of Mr Mugabe.
Supporters carried banners reading "We cannot wait until 2002", referring to the scheduled date for presidential elections.
The sizeable turnout was to be expected, again reflecting profound disillusionment with the government which failed to win a single seat in Harare.
Instability
But comments by Mr Tsvangirai came as more of a surprise.
"The time for national action is now," said Mr Tsvangirai, to enthusiastic cheers and applause, before adding: "What we would like to tell Mugabe is please go peacefully. If you don't want to go peacefully, we will remove you violently."
Speaking to journalists immediately afterwards, the opposition leader denied intending to threaten the president, saying that Mr Mugabe should simply accept the demands of the people for him to retire honourably.
He reaffirmed his party's commitment to non-violence.
Whatever the qualifications and explanations offered by Mr Tsvangirai, his remarks reflect an increasing desperation on the part of many Zimbabweans as they watch the economy continue to disintegrate after months of political instability.