Tutu`s invitation came after the Tibetan spiritual leader cancelled his visit to South Africa to receive an international award named after Mahatma Gandhi.
Dumisa Ntsebeza, the chief executive of the Desmond Tutu Peace Centre, expressed confidence that the Dalai Lama would respond positively to Tutu`s request to join him via video on Saturday for a dialogue which will replace the initially planned inaugural peace lecture by him at the University of the Western Cape as part of Tutu`s 80th birthday celebrations.
Meanwhile, the government and the ruling African National Coongress (ANC) insisted that they would have granted the Dalai Lama a visa to visit the country if he hadn`t cancelled his trip.
"Of course, he has been here before, I don`t see why it should be an issue at all," Deputy President Kgalema Motlanthe told The Star newspaper.
There was also vehement denial by International Relations Ministry spokesperson Clayson Monyela that the visa had been delayed due to pressure from China, South Africa`s largest trading partner.
The Dalai Lama this week cancelled a visit to South Africa for Tutu`s 80th birthday celebrations.
Tutu reacted by lambasting President Jacob Zuma`s government, threatening to pray for the downfall of the African National Congress.
"We betrayed our struggle; we betrayed our Constitution.
All of the people who were involved in our struggle must be turning in their graves," Tutu said in the interview, adding that the international community would have expected South Africa to side with the oppressed, considering its apartheid history.
"It isn`t anything that anyone of us can justify. The Dalai Lama is a world figure."
At the earlier media conference, Tutu warned the ANC that they would suffer the same fate as deposed rulers in Egypt and Libya.
"The trouble with the ANC, on the whole, is that they think the freedom we enjoy is due to them and everyone else is a sideline.
"Yes, they have a large majority, (Hosni) Mubarak had a large majority, (Muammar) Gaddafi had a large majority. watch out, I`m warning you, watch out. It is with love I warn you," Tutu cautioned.
Hitting out at Zuma, Tutu said his government was representing its own interests rather than representing citizens like him.
"Mr Zuma, you do not represent me, but your own interests. Our government is not representing me and is saying it will not support the Tibetans who are oppressed viciously by the Chinese."
Ela Gandhi, the South African granddaughter of Mahatma Gandhi said that if there was indeed pressure from China as was being widely believed, it would be a sad day for South Africa.