Conservative Yuriko Koike is seeking a third term with leftist Renho Murata her main challenger as the city grapples with falling birth rate

The race to become Tokyo’s next governor has kicked off, with two women in the lead to run the world’s most populous city – a rarity in a country where comparatively few women occupy high political office.

Millions of voters in Tokyo will elect their governor early next month. The successful candidate’s most urgent job has a more familiar ring, however: to address the capital’s accelerating demographic crisis.