Itcho Ito, 61, seeking re-election to a &13;fourth term in an election this Sunday, was shot at least twice in the back &13;outside his campaign office evening. Doctors said two bullets had reached his &13;heart.
Ito's death sent shock waves across a nation where gun control &13;laws are strict and violent attacks on politicians are infrequent.
Police &13;arrested Tetsuya Shiroo, 59, who they said was a senior member of a local gang &13;affiliated with Japan's largest ''yakuza'' group, the Yamaguchi-gumi, and seized &13;a revolver he had with him.
The motive for the shooting remained unclear, &13;and police declined to comment on details of the case.
Some media said &13;Shiroo had been upset at the city's handling of a traffic accident four years &13;ago in which his car was damaged as it passed a public works construction site. &13;Other reports said he had believed the city was denying contracts to a &13;construction company to which his gang was closely linked.
Prime Minister &13;Shinzo Abe denounced the shooting, as media expressed concern that the death &13;would stifle freedom of speech in campaigns for local elections across Japan on &13;Sunday.
''The atrocity committed during an election campaign is a &13;challenge to democracy and it must never be forgiven,'' Abe told reporters. ''We &13;must eradicate violence like this resolutely.''
The Asahi newspaper &13;said in an editorial that ''such base terror cannot be tolerated''.
''If &13;the use of violence is tolerated when others do not do as one says, the freedom &13;of speech will be lost. It risks pushing the country back to its wrong, dark &13;years before the war.'' Kazuo Kitagawa of the New Komei Party, junior partner in &13;the ruling coalition, told reporters: ''The candidates and parties should not &13;waver, but stoutly state their own views to voters.
''This must not have &13;any effect on the elections,'' he said.
Ito's predecessor was also shot &13;and seriously injured in 1990 by a far-right activist after he commented that &13;the late Japanese Emperor Hirohito should be held responsible for World War &13;Two.
Japan has strict gun control laws, and firearms are mostly in the &13;hands of hunters or yakuza gangsters.
Yakuza members are known for their &13;short, tightly permed hair, elaborately tattooed backs and missing little &13;fingers -- from digit-cutting rituals held to apologise for misdeeds and show &13;loyalty to the boss.
Police figures show yakuza official membership &13;numbered 41,500 in 2006, down slightly from 2005, but the number of hangers-on &13;rose marginally to 43,200.
The last known murder of a politician in Japan &13;was in October 2002, when lower house member Koki Ishii was stabbed to death by &13;a member of a right-wing group in front of his Tokyo home.
Nagasaki, on &13;the southern island of Kyushu some 1,000 km (600 miles) from Tokyo, was the &13;second city to suffer an atomic bombing by the United States, on August 9, &13;1945.
Mayor Ito was critical of US nuclear arms policies and a strong &13;advocate of Japan's sticking to its long-standing ban on nuclear &13;arms.
Last year, on the anniversary of the atomic bombing of the city, &13;Ito criticised Iran and North Korea for their nuclear programmes and had harsh &13;words for the United States for failing to halt nuclear &13;proliferation.