Campaigning has pitted environmentalists against the government and big business.
Italians are to decide whether they want to repeal a law, passed in January, that says existing concessions within 19 kilometres of the coast should remain valid until the fields are depleted, infuriating campaigners for renewable energy.
Renzi's centre-left Democratic Party (PD), keen to be seen as pro-business, has called on Italians not to vote in the hope the quorum will not be met -- sparking a backlash from opposition parties and deepening a split within his own camp.
Environmentalists claim platforms near the shore present risks to health and protected habitats. They insist a "Yes" to reversing the law would send a clear signal the country wants to go green and put a stop to "dirty deals" which benefit oil companies.
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Polling stations opened 7 AM (1030 IST) and are scheduled to close at 11 PM (0630 IST), with nearly 47 million Italians eligible to vote.
"It's a hoax referendum, they say it's about renewable energy, but actually it would mean shutting down working rigs with the loss of 11,000 jobs," Renzi said this week, with several leading political figures slamming him as a liar and criminal.
Nine regions asked for, and are affected by, the referendum, from the Basilicata, to Calabria, Sardinia and the Veneto - and nearly all of them are led by the PD, fuelling a bitter internal battle and bolstering attacks on Renzi's leadership.
"It's unacceptable for the PM to be the head of the pro- abstention party," said Roberto Speranza, a leading PD rebel.
Former president Giorgio Napolitano's unexpected defence of voter abstention this week underlined what is at stake: a "Yes" victory would be a heavy blow to Renzi ahead of a constitutional reforms referendum in October, on which the 41- year-old has bet his political career.