Police in Japan have admitted there were “problems” with security for the former prime minister Shinzo Abe, as his body arrived at his family home a day after he was assassinated on the campaign trail.

The country was in mourning for Japan’s longest-serving premier and well-wishers gathered to pay their respects, with senior politicians dressed in black arriving at Abe’s Tokyo residence on Saturday to offer condolences.

However, candidates also continued campaigning for Sunday’s upper house election, with the prime minister, Fumio Kishida, saying: “We must never allow violence to suppress speech during elections, which are the foundation of democracy.”

The murder of Japan’s best-known politician has rattled the country and sent shockwaves around the world, particularly given Japan’s low levels of violent crime and strict gun laws.

Police are still piecing together details of the man who opened fire at close range on Friday, but the 41-year-old named as Tetsuya Yamaguchi has confessed to killing the former premier, motivated by a belief that Abe was linked to an unspecified organisation.

The head of police in the Nara region where Abe was killed admitted on Saturday that there were “undeniable” flaws in security for the former leader.

“I believe it is undeniable that there were problems with the guarding and safety measures for former prime minister Abe,” said Tomoaki Onizuka, pledging a “thorough investigation.”

“In all the years since I became a police officer in 1995 ... there is no greater remorse, no bigger regret than this,” he said.

Early on Saturday afternoon, Abe’s body arrived at his home, where mourners gathered to offer prayers and flowers.

One, Tetsuya Hamada, said: “I am stunned that things like this still take place in Japan. It makes me sad. How is it possible that this happened in broad daylight?”

Japan’s upper house election will go ahead as planned on Sunday, and Kishida called on supporters to “help us until the very end”.

However, Abe’s death has cast a long shadow, and at the scene of his murder, 52-year-old Kayoko Ueda wiped away tears and described herself as “distraught”.

“I couldn’t believe something like this could actually happen in Japan,” she said.

Yamagami’s motives remain unclear, with police declining so far to identify the organisation he believed Abe had links to. They are investigating claims that Yamagami served in Japan’s navy, and said he appeared to have used a handmade gun.

The national broadcaster NHK said he described months of planning for the attack, including an initial plot involving explosives that was later shelved in favour of building guns.

Security at local campaign events in Japan can be relatively relaxed, but given Abe’s profile, questions have been raised about whether measures to protect him were too lax.

Footage of the attack showed that Yamaguchi was able to approach Abe from behind without being intercepted, and draw a weapon from a bag. He appeared to fire two shots, each producing a cloud of smoke.

Doctors who treated Abe said he sustained multiple wounds to his neck and the internal damage from the shooting reached as deep as his heart. He died of blood loss, despite receiving massive transfusions.

International reaction to Abe’s death was swift and stark, with the US president, Joe Biden, saying he was “stunned, outraged and deeply saddened” and ordering flags on US government buildings to fly at half-mast.

The Chinese president, Xi Jinping, said he was “deeply saddened” by the killing, which South Korea’s president called an “unacceptable act”.

Local media reported that a wake would be held on Monday evening and a funeral on Tuesday for close family and associates.