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Asmal, who was a minister of water affairs and forestry from 1994 and minister of education in 1999, was a member of the ANC's national executive committee.
He left Parliament and joined the University of Cape Town as professor in the faculty of law in 2008.
He died yesterday at Constantia Hospital in Cape Town due to a heart attack.
ANC spokesperson Keith Khoza said the party was saddened by the death of Asmal who served the country and the ANC throughout his life.
"We are poorer without his voice of reason."
DA leader Hellen Zille said: "Asmal will be remembered for many things, but particularly for his scholarship and his contribution to entrenching constitutionalism in South Africa.
"He left Parliament on principle, refusing to vote for the abolition of the Scorpions. He was the author of a path-breaking analysis of the chapter 9 institutions, particularly their politicisation through 'cadre deployment'.
"Unfortunately his authoritative report has still not been debated in Parliament."
IFP president Mangosuthu Buthelezi said the death of Asmal would weaken democracy.
"With his death, the Republic has lost one of the most vigilant custodians of our freedom and constitutional order," said Buthelezi.
ANC Women's League president and Education Minister Angie Motshekga said Asmal's death was a blow to South Africa.
"I was aware that he was not well but his death still left us in shock. We will miss his intellectual contribution, he was an independent thinker and was very robust in debates," said Motshekga.
National Freedom Party leader Zanele Magwaza-Msibi said: "I was impressed with his commitment in making sure that everybody has access to water irrespective of their party political affiliation."
Asmal former spokesperson while he was a education minister, Bheki Khumalo, said he was a good teacher and thoughtful leader.
"His acerbic voice of conscious and selflessness will be missed but its lessons never forgotten."
Nelson Mandela foundation chief executive Achmat Dangor said Asmal's death was a blow.
"He was a close associate of our founder, Mr Nelson Mandela, Prof Asmal struggled for decades in South Africa and in exile for an end to apartheid and for the achievement of a constitutional democracy in which all, regardless of gender, race or political affiliation would be regarded as equals."
Former Gauteng premier and deputy president of Cope, Mbhazima Shilowa said he received the news of sudden passing of Asmal with a shock and sadness.
"He always stood out as he broke ranks in defence of the foundation of our universally celebrated Constitution," said Shilowa.