Former New Zealand prime minister Helen Clark has taken her campaign to be the world's top diplomat to the Caribbean.

With rival Christiana Figueres dropping out of the race to be the next United Nations secretary-general, Miss Clark was busy in Barbados on Tuesday talking up her own credentials.

Miss Clark told an audience at a UN Development Programme event that coming from a "small country" like New Zealand meant she was fully aware of the problems facing small island nations."

"From a Caribbean perspective, you would know that you have an in-coming secretary-general who is very immersed in the issues of the small island developing states," Miss Clark said, the Jamaica Observer reported.

There is a strong push within the UN for a woman to be elected as secretary-general, something yet to be achieved in the world body's 70-year history.

However, the frontrunner after four Security Council straw polls is former Portuguese prime minister Antonio Guterres. Miss Clark finished eighth in Friday's fourth poll, with Ms Figueres, a Costa Rican diplomat, in ninth.

Speculation is also swirling Bulgaria may pull its candidate, UNESCO director Irina Bokova, who finished seventh on Friday.

There also is a push within the UN for an eastern European candidate to be elected, with that region yet to have a secretary- general.

A fifth Security Council vote will be held on September 26, with the plan to recommend a consensus candidate to the 193-member UN General Assembly in October.

Former Australian prime minister Kevin Rudd had lobbied to be part of the race, but he failed to secure Australian Prime Minister Malcolm Turnbull's support.