Serbian Prime Minister Ana Brnabic's partner gave a birth to a baby boy Wednesday, her office said, heralding it as a historic event although the conservative country does not legally recognise same-sex marriages or partnerships.

"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," her media office said in a statement.

"The delivery went well and both the mother and baby are doing fine," it added.

According to local media, the boy was named Igor.

Brnabic, 43, became one of the few openly gay government leaders in the world when she came to power in June 2017.

But she has not been a vocal advocate on LGBT issues in a country where homophobia is widespread.

In February alone there have been at least two acts of vandalism at an LGBT centre in central Belgrade.

During an appearance at a Pride parade in Belgrade in 2017, Brnabic declined to comment on whether she would like to see same-sex marriage legalised in her country.

"I can't give you my personal opinion right now because I'm here as the prime minister representing the Serbian government," she said at the time.

Although the country has various legal acts addressing gender identity and anti-gay discrimination, rights activists say that implementation is poor.

A campaign for the adoption of a law on same-sex partnerships, for which activists hope to win the premier's support, has not yet been successful.