Scrutiny, amid a whirlwind of Japanese media speculation, is now focused on the Unification Church, the Christian group known for mass marriages and efforts to cultivate relationships with conservative political parties worldwide. At a news conference on Monday, church officials outlined the organization’s ties to Mr. Yamagami’s mother, describing her as a longtime member. He had joined the church in 1998 but lost touch with the group for a long time before returning earlier this year, said Tomihiro Tanaka, head of the church’s Japan branch. The church, which did not specifically identify itself as the group cited by the police, said it had no records showing Mr. Yamagami had ever been a member and was unaware of any threats directed at its members. The church also said it had no direct relationship with Mr. Abe, although it had interacted with other lawmakers through an affiliated organization. Police have released few details about Mr Yamagami, 41, who has been charged with murder. Mr Abe was shot in the back with an improvised weapon in Nara on Friday while delivering a speech for a candidate two days before parliamentary elections. After his arrest, Mr Yamagami told police he had served in the Japanese army. A man with the same name and date of birth served three years in the country’s Navy. During a press conference on Monday, the police said Mr Yamagami confessed to testing a makeshift weapon the day before Mr Abe was shot. The police said on Friday that several improvised weapons were seized from Mr Yamagami’s apartment. The shooting shocked a nation where gun violence is rare, but during a vigil for Mr. Abe on Monday night at one of Tokyo’s largest Buddhist temples, there were few signs of increased security. Mourners coming from the street laid flowers in front of a photo of Mr. Abe. Nearby, a stream of officials in black suits and dresses filed in from nearby train stations or drove up to a guarded gate, though no one appeared to be enforcing tight security checks. The mourners gathered a day after Mr Abe’s Liberal Democratic Party won elections for the upper house of parliament. On Monday afternoon, Prime Minister Fumio Kishida praised Mr. Abe’s leadership and pledged that the newly empowered LDP would work to realize its long-held goals, including revising the country’s pacifist Constitution. The Japanese people have issued a “rousing call” to the party to ensure Mr Abe’s legacy, he said. “It is unbearable that a great leader, loved all over the world, was suddenly robbed of his life by violence.” The Unification Church was founded in South Korea in 1954 by Reverend Sun Myung Moon. He later expanded abroad, creating a network of newspapers and civic organizations that he used to develop ties with conservative political parties around the world. It also raised questions about its hiring and business practices. In the 1970s and 1980s, the group faced fundraising lawsuits and accusations of “brainwashing” by parents who said their children had been forced to join. The church established its branch in Japan in the late 1950s and soon found common cause with right-wing Japanese politicians, including Mr. Abe’s grandfather Nobusuke Kishi, over their shared hostility to communism. Ties between church-affiliated organizations and members of the ruling LDP developed over the following decades as the church grew in size and Japanese followers generated billions of dollars in revenue for the group. But the Unification Church’s influence in Japan has waned in recent decades and it has struggled to recruit new members since the split that followed Mr. Moon’s death in 2012, said Yoshihide Sakurai, a professor of sociology and religion at Hokkaido University who has study Unification. Church in Japan. Church-related groups continued to attract some top Japanese lawmakers to their events. In 2021, Mr Abe and other politicians from several countries, including the United States, spoke at a rally in South Korea run by a group linked to the Unification Church. Speaking via video, Mr Abe praised the group for its “focus and emphasis on family values”. And in 2022, during a conference in Seoul to promote peace on the Korean Peninsula, a speaker made brief written remarks on behalf of Mr. Abe. They expressed hope that the meeting would “open new avenues for peaceful reconciliation”. News of Mr Abe’s connection to the 2021 event drew criticism in Japan from the country’s Communist Party and other groups, including a lawyers’ association that has mounted a decades-long campaign against the Unification Church’s activities in Japan. In an open letter to Mr. Abe, the association, The National Network of Lawyers Against Spiritual Sales, called on the former prime minister to sever his relationship with the church and its affiliates, writing that “the cooperation and support of these events is absolutely not a good idea.” His connections with the Unification Church were probably “very weak”, Mr Sakurai said, describing Mr Abe’s remarks to the group as “business as usual for politicians who wanted to garner votes”. The church was just one of several religious organizations with right-wing political beliefs that Mr. Abe and his LDP conservatives have relied on for political support, said Levi McLaughlin, an associate professor at North Carolina State University who studies the connection between politics and religion in Japan. “None of this is unusual and certainly not exclusive,” he said, adding that “it just so happens that the church shares many of the policy platforms of the LDP and Abe in particular.” Motoko Rich and Hikari Hida contributed to this report.