The move, however, is facing opposition from Russia, and to some extent China, which are resisting attempts to change the mostly secretive selection process for the top UN post, diplomats said.
The choice of the UN chief has for decades been the purview of the five permanent Security Council members -- Britain, China, France, Russia and the United States -- in a selection process kept mostly behind closed doors.
In a bid to lift some of the secrecy, the General Assembly adopted a resolution in September that for the first time in the UN`s 70-year history asked candidates to present their resumes and lay out their vision for the job.
"One of the most important things that the UN needs to do is to choose a worthy successor to Ban Ki-moon," said British Ambassador Matthew Rycroft.
"It is a hugely important job."
Britain hopes to win backing from the council to send the letter to all 193 countries, which would be the first time that there would be a call for nominations to the top post.
The 15 council members have until Friday to decide if they support the letter, which sets deadlines for the selection.
"Those seeking the role should declare their interest in a timely manner to facilitate full participation in the process," says the draft letter, seen by AFP.
It states that the appointment should be made three to four months before January 1, 2017, to give the new secretary-general time to prepare.
Candidates should put themselves forward by the spring and the council will begin the selection process in the summer, it added.
Overcomplicated
After a first draft of the British letter was circulated last week, Russian Ambassador Vitaly Churkin complained that there was no need to "overcomplicate matters" and that the selection of the secretary-general was described in the UN charter.
The charter states that the UN chief is nominated by the Security Council and elected by the General Assembly, falling short of any specifics.
The row over kicking off the race comes amid much behind-the-scenes maneuvering over whether to choose the first woman secretary-general and picking a candidate from Eastern Europe.
Russia has said that the next UN chief should come from that region, the only one that has yet to be represented in the top job.
Among the names being floated are two Bulgarians -- UNESCO chief Irina Bokova and EU budget commissioner Kristalina Georgieva -- along with Croatian Foreign Minister Vesna Pusic.
Among non-Eastern Europeans, attention has focused on former New Zealand prime minister Helen Clark, who now heads the UN Development Program, and Chilean President Michelle Bachelet.
"There is a whole new process to select the next secretary-general," said Yvonne Terlingen of the "1 for 7 billion" campaign of NGOs lobbying for more transparency.
Terlingen said holding up the call for nominations could scuttle plans to hold hearings for candidates to make their pitch for the job, a key feature of the resolution adopted by the General Assembly.
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