President Mandela, who interceded on the issue with Colonel Muammar Gaddafi, announced he is sending his chief of staff, Jakes Gerwel, on a special flight to Libya within 48 hours to seal a deal over the trial with the Libyan leader.
The United Nations Security Council is expected to give special permission for UN sanctions against Libya to be temporarily lifted to allow the direct flight to Tripoli to go ahead.
Mr Gerwel, who is Mr Mandela's under-secretary at the South African foreign office, and the Saudi ambassador to Washington, Prince Bandar bin Sultan, are flying to Tripoli to try to secure agreement from Colonel Gaddafi for the trial to take place in The Hague.
Although there have been false dawns over the trial, the South African President and the Prime Minister signalled that it may now go ahead.
"We have made good progress," said President Mandela at a joint press conference with Mr Blair outside his state mansion in Pretoria.
The Libyan leader was close to agreement on a trial in The Hague last month, after Britain and the United States conceded his demand for it to be held in a third country, but under Scottish law, with Scottish judges.
Colonel Gaddafi objected to the two Libyan suspects having to serve any sentences in a Scottish prison. He threw in another obstacle by insisting on an international panel of judges, including a Libyan.
The Libyan leader was put under renewed pressure to back down by next month with the threat of further UN sanctions. It was not clear last night what concessions had been made, but British ministers have made clear they would not compromise over holding the trial under Scottish law, and for sentences to be served in Scotland.
Lifting sanctions against Libya would bring economic benefits to the country, which has always denied its involvement in bringing down Pan Am flight 103 over Lockerbie 10 years ago, with the loss of 270 lives.
Mr Blair said: "We have made a lot of progress on an issue which people thought was completely intractable."
The Prime Minister had urged Mr Mandela to use his personal influence with Colonel Gaddafi to find a way through the impasse and had been hoping that his visit to South Africa would herald a breakthrough.
There appeared to be a warm friendship between Mr Blair and Mr Mandela as they held a short press conference. Mr Blair paid an emotional tribute to Mr Mandela, who is to hand over office this year. "During his long political life, whether in adversity or good times, he has shown compassion, commitment, integrity, strength and forgiveness," Mr Blair said. "He has been throughout his life a shining light. I don't believe that light will ever be dimmed."
There was one area of friendly disagreement, however, over South Africa's bid to stage the World Cup in 2006 which Britain is also bidding for, with Germany. The Deputy President, Thabo Mbeki, who will almost certainly take over from Mr Mandela after elections, said it was "Africa's turn" to stage the World Cup.
Mr Mandela jokingly invited Mr Blair to be "generous" and give up Britain's counter bid. Mr Blair grinned and said: "I said there will be friendly rivalry over this."
Mr Blair has also signed an accord for possible multi-million pound defence contracts with South Africa which could generate business worth pounds 4bn. And he announced a 40 per cent increase in aid to South Africa over the next three years, totalling pounds 90m.Reuse content