Fumio Kishida led his ruling party to victory in an upper house election last month, days after Abe was shot dead by a man resentful of the Unification Church.

Since then, as the public scrutinises the church's ties with Japanese politicians and Kishida's handling of the economy, approval ratings for the government have tumbled.

They fell 13 percentage points in three weeks to 46 percent, according to a poll published Monday by public broadcaster NHK.

Political veteran Yasukazu Hamada was named defence minister -- a key role, given Kishida's pledge to ramp up the defence budget to counter growing threats from China and North Korea.

Hamada, who previously served as defence minister from 2008-9, replaced Abe's brother Nobuo Kishi, whose ailing health has prompted concern.

Kishi also recently vowed to "thoroughly review" his links to the Unification Church, after acknowledging that church members had served as campaign volunteers.

Since Abe's death a month ago, Japanese media has revealed that many ruling lawmakers -- especially those in Abe's faction -- received similar assistance from Unification Church members, something the group says followers only do as private citizens.

The organisation founded in Korea in 1954, whose followers are colloquially known as "Moonies", has confirmed that the mother of the man suspected of killing Abe was a member.

She reportedly declared bankruptcy after making donations of around 100 million yen ($1 million at the time) to the church.

On Wednesday, Kishida said he had told all his ministers to review their ties with the organisation, "so as to clear suspicion from the public".

"I appointed only those who accepted my strict instructions that each one of them check their relationship with the group and strictly review it based on their responsibility as a politician," he told reporters.

Earlier, the top government spokesman announced the new cabinet including Katsunobu Kato, who served as health minister under Abe and returns to head the ministry.

Flamboyant figure Taro Kono, who has also held several high-profile ministerial posts, was named digital affairs minister.

And Sanae Takaichi, known for her hawkish views, is the new economic security minister -- one of just two women in the cabinet.

The current foreign and finance ministers will stay in place, while Kishi has been appointed aide to the prime minister.