Italian PM Romani Prodi has said he is considering sending troops to Naples to help tackle a crime wave that has left seven people dead in five days.
Two suspected clan members on a moped were shot on Tuesday
Mr Prodi said the decision would depend on "the long-term benefits" of sending in the military.
Seven suspected members of the local mafia, the Camorra, have been arrested, following a spate of murders, daylight armed robberies and muggings.
Interior Minister Giuliano Amato said 1,000 extra police would be deployed.
He said surveillance cameras would also be installed throughout the city.
"We must radically and permanently revisit the way we defend the safety of our citizens," he said.
Tuesday was one of the bloodiest days so far in the sudden upsurge of violence.
A 36-year-old man with no record of criminality was shot and killed in his computer games store a few miles north of Naples, police said.
A few hours later, two suspected Mafia clan members were shot dead as they rode a moped south of the city.
A security services report says that blood-letting between Camorra clans who control some of the run-down suburbs could spill over into the city centre.
Some Neapolitans have been taking the law into their own hands. Last week a tobacconist shot dead a robber.
The authorities have pleaded for a long-term commitment to cut crime
The authorities are also worried about the effect on tourism - last month a Canadian was hit by a stray bullet while strolling in one of the city's squares.
The southern city - the third largest in Italy - attracts large numbers of tourists because of its history, architecture and nearby Pompeii.
The mayor of Naples, Rosa Rosso Jervolino said: "We need, above all, a major mobilisation like we had during the terrorism times in the 1970s.
"We have to fight criminals, and we need cultural and social policies of prevention. I ask the government to not forget Naples," she told the BBC.
Mr Prodi, who is due to discuss the situation in Naples on Thursday, said sending troops should not be a temporary fix.
"We have opened an analysis on the topic of the army in Naples to study the long-term benefits, because this time we won't fight just to calm public opinion for a few days or a few months," he said.
"It will be a permanent effort to ensure the safety of our citizens."
If the army is deployed it is thought likely that soldiers will not be sent on sensitive missions, but take over duties like guarding public buildings so that police officers can be freed up to fight organised crime.