By Rodrigo Campos

UNITED NATIONS (Reuters) - Former Portuguese Prime Minister Antonio Guterres is the front runner to be the next United Nations secretary-general, followed by former Slovenian President Danilo Turk, after the first U.N. Security Council secret ballot on Thursday.

According to results seen by Reuters, Irina Bokova of Bulgaria, director-general of U.N. cultural organization UNESCO came in third, edging out former Serbian Foreign Minister Vuk Jeremic and former Macedonian Foreign Minister Srgjan Kerim, who tied for fourth.

Former New Zealand Prime Minister Helen Clark, who heads the U.N. Development Programme, was fifth, followed by Slovak Foreign Minister Miroslav Lajcak, Argentinian Foreign Minister Susana Malcorra, and former U.N. climate chief Christiana Figueres of Costa Rica.

Moldova's former foreign minister, Natalia Gherman, was in 10th place, followed by Montenegro Foreign Minister Igor Luksic and former Croatian Foreign Minister Vesna Pusic.

Secretary-General Ban Ki-moon steps down at the end of 2016 after two five-year terms.

The 193-member U.N. General Assembly this year has sought to lift a veil of secrecy that has surrounded the election of the U.N. chief for the past 70 years by requiring public nominations and holding campaign-style town hall events with each candidate.

However, it is the 15-member Security Council that will choose a candidate to recommend to the General Assembly for election later this year. The council will continue to hold closed-door informal secret ballots until a consensus is reached.

On Thursday, council members were given a ballot for each candidate with the options of encourage, discourage and no opinion. The nominating states will be told of the results for their candidate, but overall results will not be made public.

According to the results, Guterres received 12 encourage, no discourage and three no opinion; Turk got 11 encourage, two discourage and two no opinion. At the opposite end, Pusic received two encourage, 11 discourage and two no opinion.

The search for a successor to Ban, a former South Korean foreign minister, has sparked a push by more than a quarter of the 193 U.N. states for the world body's first female leader, and half of the current candidates are women.

At least four members of the Security Council are part of the "Group of Friends for a woman Secretary-General" - led by Colombia - Spain, Venezuela, Japan and Uruguay. The United States and Britain are observers of the group, diplomats say.

Ultimately, the five nations that hold a veto on the Security Council - the United States, Britain, France, Russia and China - have to agree on a candidate and there is no requirement for them to pay attention to the popularity of candidates with the General Assembly. The council hopes to agree on a candidate by October, diplomats say.

British U.N. Ambassador Matthew Rycroft told reporters on his way into the council that the purpose of the secret ballots was to "encourage people who don't do so well to drop out of the race."

(Additional reporting and writing by Michelle Nichols; Editing by James Dalgleish and Leslie Adler)