Sunday`s poll is part of the Italian public`s right to scrap pieces of legislation by referendum, but the outcome is valid only if at least 50 percent of eligible voters take part.
Vote `not needed`
Prime Minister Matteo Renzi said he would abstain from voting and urged the public to boycott the poll, arguing that ending drilling rights would increase Italy`s dependence on imported energy, which currently stands at 90 percent.
Renzi also warned that 11,000 jobs would be lost and the economy would weaken if the referendum was approved.
The amount of resources at stake is equal to three percent of Italy`s annual domestic demand for gas and one percent of annual demand for oil.
Regional power tussle
The referendum was declared after nine regional governments - most of them run by Renzi`s own center-left Democratic Party - campaigned to wrestle some influence over energy policy away from the central government in Rome.
They vowed action in December when Renzi`s administration extended all existing 30-year concessions within 12 kilometers (7.5 miles) off shore until resource exhaustion.
Unlikely to pass
Analysts said despite the backing of environmental groups and opposition parties, the vote was liked to be declared void due to a low turnout.
But they conceded it would be a blow to Renzi if substantial numbers did turn out, and may be seen as a political snub just weeks before major local elections.
The vote is also seen as a trial run for another referendum due in mid-October, which will see Renzi square off against the same opposition parties over major constitutional reforms he has recently pushed through parliament.
Environmental watchdog Legambiente and other green groups say domestic oil and gas production is minimal and that continued focus on fossil fuels takes Italy further away from its renewable energy and carbon targets.
Polling stations opened at 7 am local time (05:00 UTC) on Sunday and were due to close at 11 pm. The results were likely to be declared within a few hours.
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