Officials have blamed the problem on organised criminal gangs that have taken over rubbish collection services and disorganised bureaucracy.
Rosa Russo Iervolino, the mayor of Naples, called on the "overwhelming majority" of people in Pianura to remain calm after many residents went on the rampage against the planned reopening of a waste dump, closed in 1996.
Residents fear the reopening will harm their health and about 150 people blocked the entrance to the dump to prevent trucks carrying building materials from entering.
They were finally allowed through after police intervened.
Iervolino said she sympathised with the residents because garbage collectors have not been picking up the rubbish since December 21.
A number of residents have been setting piles of rubbish on the streets ablaze on the streets and firefighters had to put out more than 80 of the them overnight and another 40 during the day, fire authorities said.
Giorgio Napolitano, the Italian president, said he was "alarmed" by the situation and called on officials to make sure the situation is resolved.
Rubbish pileups because of shortage of space in dumps have plagued the port city sporadically for several years.
Premier Romano Prodi told journalists in his hometown of Bologna that Naples' garbage problems needed to be solved "once and for all," adding that government ministers would meet on Monday over the issue.
"Everybody's watching us, and I don't want Italy to give off this negative image," he said.