Local officials said the man, who was later shot by police and arrested, opened fire on passersby mid-morning in downtown, close to the main post office and railway station, and then turned his weapon on police.
The Tours government office identified the man as a 44-year-old worker for the SNCF state railway and said he may have had a grudge against his employers.
Police sources said the man had been questioned in the hospital, but his answers were incoherent.
A witness told France's LCI television that a man wearing a ski mask had fired on passersby in the center of town, stopping to reload his weapon.
Three passersby were killed near the city's main post office, police said. Another person was killed near the train station.
Television film showed armed police leading the man, dressed in a brown leather jacket and jeans, away from the entrance to an underground parking in handcuffs with blood on his hands.
Armed police, including some 30 members of the crack RAID squad which deals with major shootings and hostage takings, evacuated the city center and surrounded the parking lot.
Suspicions that an alleged accomplice may have fled into the parking turned out to be unfounded, police said, but the premises were being searched for any explosives.
Jospin, speaking in the northern city of Rennes where he was on a visit, said the gunman appeared to have been deranged.
"The person who opened fire does not appear to have any criminal record," Jospin told reporters. "It seems to be someone working in the public sector who went crazy."
Local officials identified the dead as four men, between ages 33 and 66. None of the wounded, who included three police officers, was in serious condition.
French security forces have been on high alert since the Sept. 11 hijacked airliner attacks on the United States.
France has increased the number of police and security forces in city centers under an anti-terrorism plan first used in the mid-1990s during bomb attacks by Algerian militants.
Jospin denied there had been a security lapse.
"When someone, if this is the case, is seized by an act of murderous madness, that's not a matter of ordinary security. I don't think the two things should be mixed up," he said.
One of France's police unions, the UNSA, said the shooting highlighted the need for tougher weapons legislation in France, where hunting is a popular pursuit. It called in a statement for the creation of a national register of gun owners.
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