Fan died yesterday evening at his apartment in the company of priests and lay people following a brief illness, the US-based Cardinal Kung Foundation and the unofficial website chinacath.Org reported.
The Kung Foundation said officials in Shanghai, China's financial hub, turned down a request to hold his funeral at the city's cathedral and would only permit a small service at a funeral home.
Fan was named Shanghai bishop by Pope John Paul II in 2000, but was refused recognition by the Communist Party-controlled Catholic Patriotic Association that oversees the church in China. Fan was immediately placed under house arrest and another priest, Aloysius Jin Luxian, was named bishop.
China has an estimated 8 million to 12 million Catholics, around half of whom worship in congregations outside the control of the Catholic Patriotic Association.
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Jin's successor, Thaddeus Ma Daqin, has not been seen in public since being taken into custody in 2012 after declaring his withdrawal from Catholic Patriotic Association at his ordination ceremony, shocking and angering officials. He is believed to be held at Shanghai's Sheshan Seminary.
Although Beijing later rescinded Ma's appointment, the president of the Kung Foundation, Joseph Kung, said Fan's passing reinforced the need for Ma's release and return to pastoral duties, a move that would finally unite the government-approved and underground congregations.
A man who answered the phone at the Shanghai Diocese said he had heard of Fan's death, but said no official statement would be issued. The man gave only his surname, Hu, as is common among Chinese bureaucrats.
Born in 1918, Fan was baptised a Catholic in 1932 and ordained a Jesuit priest in 1951, two years after the Communists seized power.
Arrested in 1955 after Communist leader Mao Zedong ordered Chinese Catholics to cut all ties with the Vatican, he was sentenced to 20 years in prison for counter-revolutionary crimes and forced to work at a labour camp mortuary in the remote western province of Qinghai.