Yasuhide Mizobata fled into an apartment building on Tuesday afternoon after firing repeatedly at officers who challenged him, a force spokesman said.
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He spent the night holed up in the building, surrounded by heavily-armed police who were trying to convince him to surrender.
Television footage showed Mizobata, clad in a black shirt and pants and white shoes, brandishing two pistols as he stood atop scaffolding.
Media reports said the suspect had threatened to shoot police and turn the gun on himself during the overnight standoff in Wakayama, 450 kilometres (280 miles) southwest of Tokyo.
Broadcasters said the building had been evacuated as the incident began and there are not believed to be any hostages.
A massive manhunt began on Monday after Mizobata allegedly killed 45-year-old Junsuke Ishiyama and wounded three others when he opened fire during a meeting at the offices of a construction company.
Mizobata is reportedly the son of the company owner.
He had been scheduled to go to jail on Monday after having been convicted of drugs charges, the Sankei Shimbun daily said.
Since Monday's incident, local officials have warned residents to stay indoors.
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Gun violence is exceedingly unusual in Japan, where there are very strict controls on firearms ownership.
In 2015, there were just eight reported gun crimes nationwide, the National Police Agency has said, with one person killed and three wounded.
The few weapons in circulation are often linked to organised crime.
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