Italians voted Sunday against the advice of coronavirus experts in a referendum and regional elections that could weaken the government and radically reshape the political landscape.

Just a week after a Herculean effort by schools to reopen in line with last-minute Covid-19 rules, classrooms nationwide were transformed into polling stations for the two-day vote.

In the early evening, voter turnout was estimated at 30 percent.

A triumph for the far right in the fiercely fought campaign would ring alarm bells in Brussels.

It is the first test for Prime Minister Giuseppe Conte's centre-left coalition government since it imposed an economically crippling nationwide lockdown to fight the virus, which has claimed nearly 36,000 lives.

The referendum, on slashing the number of members of parliament -- from 630 to 400 in the lower house, and 315 to 200 in the upper house -- is expected to pass, though the number of prominent "no" declarations has seen a late uptick.

Italy has Europe's second biggest parliament after Britain with around 1,400 members and ahead of France, which counts 925.

The cost-cutting reform is the brainchild of the co-governing Five Star Movement (M5S), but while its centre-left coalition Democratic Party (PD) partner and parties on the right are theoretically in favour, their support has been lacklustre at best.

- Uncertain future -

The regional battle is for the governance of Campania, Liguria, Marche, Puglia, Tuscany, Valle d'Aosta and Veneto.

In every region, Matteo Salvini's far-right League, the anti-immigration, anti-LGBT Brothers of Italy and former prime minister Silvio Berlusconi's Forza Italia have formed a right-wing coalition.

The grouping is set to easily retake Veneto and Liguria, and could also snatch Marche and Puglia from the left.

All eyes will be on Tuscany however, a historically left-wing stronghold that might fall to the far right.

A nun leaves after casting her vote in Rome / © AFP

"If the left performs particularly poorly... Brussels will grow concerned," Berenberg economist Florian Hense told AFP.

The EU will worry whether the national recovery plan that Italy must present to obtain grants or loans to aid its ailing economy "will be ambitious enough, given the limited political capital of the coalition in Rome," he said.

"And whether, whatever plan Italy comes up with, it will actually implement it given the uncertain future of the current coalition", Hense added.

- Concern over virus -

The vote took place despite warnings against opening polling stations while Covid-19 cases are on the rise.

While Italy is seeing fewer new cases than Britain, France or Spain, it still recorded some 1,600 cases on Saturday as well as 15 deaths.

"The country is in a state of emergency; it is utterly contradictory to be massing people together at polling stations, particularly in light of the trend in Europe," Massimo Galli, infectious diseases chief at Milan's Sacco hospital, told AFP.

But Rome student Lorenzo Salvioni said he hoped "the country's difficulties caused by Covid" would mobilise the vote.

Some precautions have been taken, with elderly and pregnant voters getting fast-track lanes to cast their ballot.

With older people potentially put off voting by the health risks, the left has been organising special transport.

One in three voters for the PD and League are over 65 years old, according to Italy's Corriere della Sera daily.

Nearly 2,000 voters who are in isolation because of the pandemic have registered to have their votes collected, including Berlusconi, who turns 84 late this month.

The media magnate and former PM contracted the virus but left hospital last week.

But fear of catching the virus has seen a flurry of last-minute desertions by polling station volunteers.

Milan was forced Saturday to call urgently for 100 fresh pairs of hands.

Prime Minister Conte has clinched a deal behind closed doors with PD leader Niola Zingaretti to fight to save each other's political skins should the left perform disastrously, according to the Repubblica daily.

But that might not be enough.

"These elections are not going to topple the government," political commentator Barbara Fiammeri for Italy's Il Sole 24 Ore daily told AFP.

"But there could well be a crisis, whether it be Conte's fall, the forming of new coalition, or even a national unity government".