Dr Kalim Siddiqui died in Pretoria, South Africa, where he had been attending an Islamic conference.
Dr Muhammad Ghayasuddin, spokesman for the 150-member parliament, said: "He was a great leader who was loved and respected by millions of people all over the world."
Last month Dr Siddiqui said the death sentence against Rushdie, pronounced by the late Ayatollah Khomeini, must stay in force.
His remarks were understood to contrast sharply with an apparently softer line on the issue recently adopted by Iran.
Dr Siddiqui was one of the founder members of the Muslim Parliament of Great Britain, leading the group since it was set up in 1992. The parliament aims to represent the views of Muslims living in Britain.
He lived in Slough, Berkshire.Reuse content