BBC reported Thursday that Tsvangirai said the "acrimony is over" between him and Mugabe.
The remark came ahead of a tour of Europe and the United States aimed at garnering support for Zimbabwe's four-month-old power-sharing government.
Tsvangirai is to meet with, among others, U.S. President Barack Obama and British Prime Minister Gordon Brown. The country is needs $45 billion in the next five years to help revive the African nation's economy after years of political strife.
Zimbabwe's unity government between the former bitter enemies was inaugurated in February, ending months of political crisis following disputed elections.
"We hope the gains we've made so far will convince even the most skeptical this government is consolidated," Tsvangirai was quoted by the British network as saying.
Tsvangirai said he and the longtime president have a "workable relationship," BBC reported.
"If we have differences they are expressed in a respectable way," said Tsvangirai, leader of the Movement for Democratic Change party.