When Tetsuya Yamagami was apprehended following the assassination of Japan’s former Prime Minister Shinzo Abe, he told police he had “a grudge” against a “certain group.” However, authorities have not identified the organization or explained its relationship to Mr. Abe.

Scrutiny is now focused on the Unification Church, a Christian organization known for mass weddings and efforts to cultivate relationships with conservative political parties around the world.

Church officials detailed the organization’s ties to Mr. Yamagami’s mother, describing her as a longtime member, at a news conference on Monday. She had joined the church in 1998 but had lost contact with it for a long time before returning earlier this year, according to Tomihiro Tanaka, the head of the church’s Japan branch.

The church, which did not specifically identify itself as the group cited by the police, stated that it had no records indicating Mr. Yamagami had ever been a member and that it was not aware of any threats directed at its members by him. The church also stated that it had no direct relationship with Mr. Abe, but had interacted with other legislators through an affiliated organization.

Mr. Yamagami, 41, has been charged with murder, but police have released few details about him. Mr. Abe was shot from behind with a homemade gun while delivering a speech for a candidate in Nara on Friday, two days before a parliamentary election.

Mr. Yamagami told police after his arrest that he had served in the Japanese military. A person with the same name and date of birth served in the country’s Navy for three years.

During a news conference on Monday, police said Mr. Yamagami admitted to testing an improvised weapon the day before Mr. Abe’s shooting. The police said Friday that they had seized several improvised guns from Mr. Yamagami’s apartment.

The shooting shocked a country where gun violence is uncommon, but there were few signs of increased security at Mr. Abe’s wake on Monday night at one of Tokyo’s largest Buddhist temples. Mourners passing by on the street left flowers in front of a photograph of Mr. Abe. A stream of dignitaries in black suits and dresses walked in from nearby train stations or arrived by car at a guarded gate nearby, though no one appeared to be imposing strict security checks.

Mourners gathered one day after Mr. Abe’s Liberal Democratic Party swept to victory in Upper House elections. Prime Minister Fumio Kishida praised Mr. Abe’s leadership on Monday afternoon, promising that the newly empowered L.D.P. would work to realize his long-held goals, including revising the country’s pacifist Constitution.

Rev. Sun Myung Moon founded the Unification Church in South Korea in 1954. It later expanded internationally, establishing a network of newspapers and civic organizations through which it developed relationships with conservative political parties all over the world. It also raised concerns about its hiring and business practices. In the 1970s and 1980s, the group was sued for soliciting funds and accused of “brainwashing” by parents who claimed their children were coerced into joining.

In the late 1950s, the church established a branch in Japan, and it quickly found common cause with right-wing Japanese politicians, including Mr. Abe’s grandfather Nobusuke Kishi, in their shared hatred of Communism.

Ties formed between church-affiliated organizations and members of the ruling L.D.P. in the decades that followed, as the church grew in size and Japanese followers generated billions of dollars in income for the group.

However, the Unification Church’s influence in Japan has dwindled in recent decades, and it has had difficulty recruiting new members since a schism following Mr. Moon’s death in 2012, according to Yoshihide Sakurai, a Hokkaido University professor of sociology and religion who has studied the Unification Church in Japan. Church-related organizations have continued to attract top Japanese lawmakers to their events.

Mr. Abe and other politicians from various countries, including the United States, spoke at a gathering in South Korea organized by a Unification Church-affiliated group in 2021. Mr. Abe, speaking via video feed, praised the group for its “focus and emphasis on family values.”