President Robert Mugabe and opposition leader Morgan Tsvangirai have signed a deal outlining a framework for talks on Zimbabwe's political crisis. It says that talks on a power-sharing arrangement should be completed within two weeks of its signing. Discussions will focus on security, and the political and economic priorities of the new government. Mr Mugabe and Mr Tsvangirai have been locked in a bitter dispute over this year's presidential polls. Under the terms of the agreement, each party will be expected to do everything possible to stop all forms of political violence and refrain from making inflammatory statements. The BBC's southern Africa correspondent Peter Biles, in Johannesburg, says the deal is a breakthrough, even if it is only a first step. He says Mr Mugabe seemed to be in conciliatory - and sometimes good-humoured - mood as he made the unprecedented move of appearing with his arch-rival in front of the media. Mr Mugabe insists that he must be recognised as Zimbabwe's president - a position rejected by the opposition Movement for Democratic Change (MDC). Mr Tsvangirai, the MDC's leader, garnered more votes in an initial presidential poll in March, but election officials said there was no outright winner and called for a run-off. Mr Mugabe won the run-off - but he was the only candidate after Mr Tsvangirai withdrew, accusing the government of mounting a campaign of violence against his supporters. 'Bitter words' The document was signed at a Harare hotel during the first meeting between Mr Mugabe and Mr Tsvangirai in a decade. The pair then shook hands. Arthur Mutambara, who leads a breakaway faction of the MDC, also signed the agreement. Mr Tsvangirai said that in signing the deal - an occasion he described as historic - he and Mr Mugabe were committing themselves to the "first tentative step towards searching for a solution". He said many "bitter words" had been exchanged, but all all parties must exercise tolerance and work together if they wanted progress. Mr Mugabe said the two sides had agreed that the country's constitution needed to be amended on various points. "We sit here in order for us to chart a new way, a new way of political interaction," he said. Mr Mugabe praised South Africa's President Thabo Mbeki, who helped broker the deal, but insisted that it would be Zimbabweans who resolved the crisis - without the influence of Europe or the US. He has previously accused Mr Tsvangirai of being a puppet of Western powers - particularly the UK, Zimbabwe's former colonial master. A US state department spokesman said it supported any talks that would lead to a result reflecting the "will of the Zimbabwean people". UN Secretary-General Ban Ki-moon said he welcomed the deal and urged all sides "to engage, in good faith, in serious talks that would lead to a lasting solution". Jean Ping, chairman of the African Union (AU), congratulated the parties on the deal and encouraged them to "build on this positive development". New elections call The MDC has previously accused Mr Mbeki of being biased in favour of Mr Mugabe. The fact that the AU and United Nations joined the South African mediation efforts was crucial in persuading the opposition party to agree to talks, analysts say. Diplomats from the Southern African Development Community (Sadc) were also involved. The MDC has set out several conditions to be met before starting substantive talks with Mr Mugabe, including the complete cessation of violence and the release of all political prisoners. It wants some kind of "transitional authority" to organise new, internationally-monitored elections. The MDC says at least 120 of its supporters have been killed, about 5,000 abducted and 200,000 forced from their homes since the first round of the elections, in a campaign of violence by pro-Mugabe militias and the army. Cabinet ministers and military officials have denied the charges.