"Italy is a country of culture and so I challenge businessmen. What are you waiting for?" Matteo Renzi told journalists when quizzed on the future of the ancient site, where several walls collapsed this weekend.
"The ideological refusal to permit the private sector to intervene, as if only the public sector could guarantee the guardianship of heritage, must
end," he said.
"If the private sector can keep the wall standing upright, why not allow it to?" he added.
The culture sector in Italy has suffered from harsh budget cuts and a deep recession and funds for culture are expected to be cut further to €1.4 billion for 2014, from €1.5 billion a year earlier.
The government has already called on the private sector to help restore other of its UNESCO monuments: in Rome, luxury shoemaker Tod's is financing works at the Colosseum, while high-end fashion house Fendi is expected to refurbish the Trevi Fountain.
Collapses at Pompeii's Temple of Venus and other ancient buildings this weekend sparked fresh international anger at the slow pace of a multi-million EU-backed project to restore the famous Roman site.
Culture Minister Dario Franceschini has said he will unblock some €2.0 million euros ($2.8 million) to "get the machine working" and save the complex.
Last year, conservation workers began a 105-million-euro makeover of Pompeii, funded by the EU to the tune of 41.8 million euros.
But according to the Corriere della Sera daily Tuesday, only €588,000 has been spent so far - just 0.56 percent of the funds.
The project is seen as crucial to the survival of Pompeii after a series of collapses at the 44-hectare site in the shadow of Mount Vesuvius - the
volcano that destroyed the city in 79 AD.