Last week Iran's religious establishment named Ayatollah Sheikh Muhammad Ali Araki, who is in his nineties, as Golpayegani's successor. While he might be qualified for the job, many leading Shias both inside Iran and elsewhere fear the appointment of Ayatollah Araki would pave the way for his eventual replacement by Iran's strongman and spiritual leader, Ayatollah Ali Khamenei.
The row over the succession risks straining relations between Iran and the radical Shia groups it supports, including Hizbollah in Lebanon and the Iraqi opposition group, Al-Dawaa, based in Tehran.
At Friday prayers yesterday, Iran's chief justice, Ayatollah Muhammad Yazdi, called for Mr Khamenei to be designated as the sole leader of the world's Shia Muslims. Most Shias live in Iran, Iraq, Lebanon and Pakistan.
If Mr Khamenei filled the post, the fusion between religious and political authority would be complete for the Islamic Republic of Iran. No one has fulfilled the dual functions of both spiritual and religious leader there since the death of Ayatollah Ruhollah Khomeini in 1989.
After his death, the most senior ayatollah in Iran was Golpayegani, who was based in Iran, and the most senior worldwide was the late Grand Ayatollah Abulqassem al- Khoei, based in Najaf in Iraq, who died in 1992.
Since 1992, the governments of both Iran and Iraq have sought to intervene in the selection of the successors to these figures.
Shia leaders are traditionally chosen not by governments but through a long process held by different communities. Furthermore, Mr Khamenei is not acceptable to many because of his lack of academic qualifications in theology, owing to his pursuit of politics.
Over the past days, the authorities in Iran have detained hundreds of supporters of dissident grand ayatollahs in Tehran and the cities of Mashad and Qom, according to information coming out of the country.
Reports from Tehran say the holy city of Qom, regarded as the cradle of militant Islam and home to many of the world's grand ayatollahs, is under virtual martial law. 'Ever since members of the Golpayegani family refused to allow Ayatollah Khamenei to lead the funeral ceremonies, tension has been very high in Qom, and fighting has erupted between followers of senior ayatollahs and the revolutionary guards,' according to Dr Mehdi Haeri, a dissident ayatollah teaching in German universities.
At the same time, Tehran has warned the Lebanese Hizbollah that it will lose vital financial assistance from Iran unless the organisation's leadership officially announces its 'full allegiance' to Mr Khamenei.
The Shia community is deeply divided over the question of its leadership, split between those who follow Iran's political-revolutionary line and the conservatives who insist on the separation between religion and politics.
Sheikh Muhammad Fadlallah, the spiritual leader of Hizbollah in Lebanon, backs the candidacy of Ayatollah Syed Ali Seestani of Najaf, as do the influential Khutaba community in India, Shias in Saudi Arabia, and many of the Shia clerics imprisoned by the Iraqi regime.