The focus is on the Italian capital Rome where incumbent rightwing mayor Gianni Alemanno is running virtually neck-and-neck in the most recent opinion polls with leftist challenger Ignazio Marino.
The polls are also a key bellwether of support for the anti-establishment Five Star Movement, which won a quarter of the vote in national elections but has appeared to lose ground since then.
Polling stations will re-open on Monday for a second day of voting and close at 1300 GMT, with preliminary results expected later in the day.
Second-round run-off votes will be held on June 9-10, with most analysts predicting the Rome mayoral race will not be won on the first round.
Alemanno has come under fire in the Eternal City for traffic-clogged streets, a waste disposal crisis and a drop in tourist arrivals.
He has defended himself saying he inherited a debt-riddled city from leftist mayors before him and pointing to key projects he has backed.
Marino has promised to do more to improve public transport and to ease the social crisis brought on by record-high unemployment levels in the city.
The elections affect 564 local authorities, including the cities of Ancona, Brescia, Pisa and Siena -- many of them facing similar problems brought on by a grinding recession.
The centre-left Democratic Party narrowly came first in elections in February against Silvio Berlusconi's centre-right People of Freedom party but failed to win a majority in parliament.
A two-month deadlock ensued which was only resolved last month with the start of an unprecedented grand coalition government bringing the two parties and former prime minister Mario Monti's centrists together in the cabinet.
Some analysts predict Berlusconi could bring down the government within months, triggering fresh elections that polls indicate his party would win.
But the three-time former prime minister, who is facing a series of legal battles including charges of tax fraud and paying for sex with an underage prostitute, has insisted that he will support the government.