Japanese Prime Minister Shinzo Abe has denounced the murder of Nagasaki's mayor Itcho Ito as unforgivable.
Mr Ito was shot outside a train station in central Nagasaki
Mr Ito was shot in the back outside a train station on Tuesday evening, and died early on Wednesday in hospital.
"This murder, which took place in the middle of an election campaign, is a threat to democracy," said Mr Abe.
Police said they had arrested a man named Tetsuya Shiroo, who is alleged to be a member of one of Japan's leading criminal groups, the Yamaguchi-gumi.
Japanese media said the murder appeared to be linked to an alleged controversy over the city's handling of a traffic accident four years ago.
The attack has shocked people in Japan - a nation which sees little gun crime and where handguns are strictly banned.
"We are truly saddened by the passing of Mayor Ito," Nagasaki's Vice Mayor Nobuhiro Uchida said in a statement on Wednesday.
"We could never forgive such a cowardly act and we feel strong indignation."
"It cannot be forgiven no matter what," Mr Abe added. "We have to show our strong determination to get rid of such violence."
Mr Ito was shot while out campaigning for re-election for a fourth term as mayor of the southern city - which is best known worldwide for being virtually flattened by a US atomic bomb in the closing days of World War II.
Paramedics treated him on the ground before he was taken to hospital in an ambulance. Doctors worked for several hours to keep him alive but he died at 0228 on Wednesday (1728 GMT Tuesday).
One of the bullets had reached his heart, hospital officials said.
Despite the fact that gun violence is rare in Japan, Nagasaki has seen attacks on politicians before.
Mr Ito's predecessor Hitoshi Motoshima was shot and seriously injured in 1990 by a right-wing extremist, after he said that Emperor Hirohito bore some responsibility for World War II.