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Serbian Prime Minister Ana Brnabic's gay partner has given birth in what the PM's office said was a first for a world leader.

A statement said the birth mother, Milica Djurdjic, and baby, reportedly a boy named Igor, were "doing fine".

Ms Brnabic, 43, became both Serbia's first female and first gay prime minister in June 2017.

Her appointment was seen as a surprise move for the Balkan nation where same-sex marriage is not recognised.

"Ana Brnabic is one of the first prime ministers whose partner has given birth while in office... and the first in the world in a same-sex couple," the AFP agency quoted her office as saying.

Ms Djurdjic, who works as a doctor, became pregnant though artificial insemination. She and Ms Brnabic met at a gay bar in the capital, Belgrade.

Serbia is socially conservative and homophobia is common.

The country's constitution explicitly defines marriage as being between a man and a woman, and gay civil partnerships are not officially recognised.

Same-sex couples are also barred from adopting children, though single people can adopt regardless of their sexual orientation.

Serbia has several laws in place to tackle discrimination, inequality and hate speech, but activists argue that not enough is being done to expand these rights or enforce them.

Critics have spoken out against Ms Brnabic, arguing that she has not done enough to bolster LGBT rights.

At a Gay Pride parade in Belgrade in 2017, she refused to say if she would like to see same-sex marriage legalised in Serbia.