Colonel Muammar Gaddafi fell out with Robert Mugabe when the Zimbabwean dictator backed Ugandan leader Yoweri Museveni to thwart his ambitious project for a United States of Africa.
Before going to Libya, Tsvangirai visited Morroco, the only African country to openly declared hostility with the South African government over its recognition of Saharawi Arab Democratic Republic. Tsvangirai also visited Algeria and Tunisia.
Tsvangirai and his arch-rival Mugabe joined forces nine months ago in a coalition to try to end a decade-long political and economic crisis, but their government has proved shaky because of their failure to agree on the implementation of parts of the unity agreement.
Last month, Tsvangirai’s Movement for Democratic Change (MDC) announced it was "disengaging" from the government but rejoined three weeks later after mediation by the Southern African Development Community (SADC).
The MDC leader said he was going to Morocco for diplomatic engagements and would also meet Gaddafi, chairman of the African Union (AU), during his five-day trip to North Africa.
"The AU is one of the guarantors of the GPA (Global Political Agreement) so I am taking advantage of being in that region to brief the chairman of the AU on the developments in the country, what progress we are making and SADC’s progress in dealing with the outstanding issues," he told journalists.
Political analysts say Tsvangirai’s talks with the AU chairman will help him to maintain diplomatic pressure on Mugabe to honour the power-sharing agreement. Mugabe and Gaddafi have strong political ties.
Tsvangirai said on Thursday talks between the MDC and Mugabe’s ZANU-PF party would continue to try to solve differences and to meet a December 5 deadline set by the 15-nation SADC.
He said he had been invited by Gaddafi and was expecting "significant progress" from the MDC-ZANU-PF talks.
Asked whether the rival Zimbabwean politicians would be able to reach an agreement by the deadline set by SADC, Tsvangirai said: "The deadlines are not set in stone … the whole urgency of the matter is to rescue the credibility of the inclusive government."
He added: "I am hoping that by the time I come back there is significant progress."
Besides refusing to allow some of its members to be sworn into government, the MDC accuses ZANU-PF — which it calls an "arrogant and unreliable partner" — of persecuting its officials and delaying media and constitutional reforms needed for free and fair elections to be held in about two years’ time.