The president of the World Bank has traditionally been an American under an informal agreement dating to the founding of the bank 68 years ago - campaigners want this changed

The old alliance of Europe and America faces a huge row with the rest of the world over the identity of the next head of the World Bank, after president Robert Zoellick said on Wednesday he is to leave his post in June.

While his departure had been widely expected, the news kicks off the process of finding a new leader, who has traditionally been an American under an informal agreement dating to the founding of the bank 68 years ago. Speculation has focused on either US Secretary of State Hillary Clinton - who is also rumoured to have an eye on a run for the White House - or former Treasury secretary Larry Summers as Zoellick's likely successor. When Dominique Strauss-Kahn was succeeded by his countrywoman Christine Lagarde at the International Monetary Fund last year, it was widely rumoured that America had agreed to let Europe keep its traditional grip on the IMF – in the face of calls for a candidate from an emerging country – as long as France and other European governments backed Clinton as the new boss of the World Bank when the job came up.

However, calls to widen the search to include candidates from outside the US began immediately. Campaigners including Oxfam, Eurodad and the African Forum and Network on Debt and Development (Afrodad), issued a joint statement appealing to America not to continue its monopoly of the role.

Elizabeth Stuart of Oxfam said: "The way the World Bank picks its president needs to change. The bank only operates in developing countries, so any candidate not supported by a majority of these countries would plainly lack legitimacy."

In an open letter to governors of the World Bank, which provides loans to developing countries for capital programmes, the campaigners demanded that: the new president is selected by a majority of World Bank member countries; that the selection process is open to anyone to apply; and that a clear job description and required qualifications is set out, including "a strong understanding and experience of the particular problems facing developing countries".

The search for Zoellick's successor now begins under guidelines adopted in 2011 that call for an "open, merit-based and transparent selection" process.

While that may suggest a break from the informal agreement that the bank's president is always American, World Bank observers say that the rule has merely motivated the US to put forward strong candidates, who it can be convincingly argued might be the best person for the job.

Clinton's name has continued to circulate as one of those, despite apparently ruling herself out of the job when asked last year. She has repeatedly said she has no plans to stay on as secretary of state past the end of President Obama's first term.

Zoellick agreed that it was important that the process to select his successor was fair. But asked by Reuters whether the US government would agree to open up the selection process he replied "you'll have to ask them". He added that rumours he might now work for the Republican Party were "not true".

The World Bank said that under Zoellick, who will have served one full five-year term, it had "played an historic role during the global economic crisis, using record replenishments to provide more than $247bn to help developing countries boost growth and overcome poverty."