Fatima Ezzahra El Mansouri, whose party won last week's parliamentary elections, called the appointment a 'source of pride' for women.
El Mansouri becomes only the second woman to serve as prime minister in the Arab world.
Serbian President Aleksandar Vucic has resigned and is expected to run for prime minister, according to a breaking report.
The prime minister told the BBC that an early poll would throw the country into a 'backward-looking process.'
Burnham faces pressure to set out a clear vision for the country as he takes centre stage at his first party conference as PM.
The 44-year-old economist and European People's Party vice-president has been put forward for the role, according to Anadolu Agency.
BBC Politics reports on the prime minister's debut in Parliament, which came more than six weeks after he took office.