Sanae Takaichi, named Japan's first woman prime minister on Tuesday, said her priority was to tackle inflation – a major source of anger among voters.

Japan's fifth premier in as many years leads a minority government and has a bulging in-tray, not least the scheduled arrival of the US leader next week.

But in her first remarks in office, she said she would soon draft an "economic package" to deal with rising prices.

The former heavy metal drummer and Margaret Thatcher admirer became head of the Liberal Democratic Party (LDP) on October 4, but its coalition collapsed days later.

This forced Takaichi to form an alliance with the reformist, right-leaning Japan Innovation Party (JIP), which was signed on Monday.

She was approved by parliament as prime minister on Tuesday and formally took office.

Her first challenge will be US President Donald Trump's visit to Tokyo in the coming days, during which she plans to have "candid discussions" on bilateral issues as well as the broader Asia-Pacific region, the Middle East, and Ukraine.

"I want to build relationships of trust," she told journalists.

Being in a minority in both houses of parliament, the new coalition will need support from other parties to push through legislation.

Takaichi previously said that "Japan is completely looked down on by China", and that Tokyo must "address the security threat" posed by Beijing.

But she has since toned down her rhetoric, and last week stayed away from the Yasukuni shrine that honours Japan's war dead, long a flashpoint in Tokyo's regional ties.

The Foreign Ministry on Tuesday urged Tokyo to "honour its political commitments on major issues including history and Taiwan".

EU chief Ursula von der Leyen congratulated Takaichi for "making history" as Japan's first woman premier.

Takaichi had promised a cabinet with "Nordic" levels of women, up from two under predecessor Shigeru Ishiba. The record for Japan is five.

But she named only two other women in her 19-strong cabinet, with Satsuki Katayama in charge of finances and the Japanese-American Kimi Onoda taking on the economic security portfolio. (AFP)