Ms. Takaichi would be Japan’s first female prime minister in a country where women are drastically underrepresented at the highest levels of power.

She was elected LDP president on Saturday after winning a run-off vote against Shinjiro Koizumi, the son of a former prime minister.

Takaichi is a long-time admirer of Margaret Thatcher, but many female voters do not see her as an advocate for progress.