France's municipal elections saw record-low turnout on Sunday as coronavirus fears kept millions of voters from polling stations, prompting calls to cancel the second round of voting as authorities scramble to curtail the outbreak.

Polling institutes estimated the abstention rate at 54 to 56 percent, nearly 20 points higher than the previous record set in municipal votes six years ago.

France is set to choose mayors for 35,000 town halls and almost half a million councilors in a vote overshadowed by the coronavirus outbreak.

The government on Saturday ordered the shutdown of most shops, restaurants and entertainment facilities and urged people, especially those over 70, to stay at home after the number of coronavirus cases doubled in 72 hours.

However, the government had rejected calls to cancel the first round municipal voting, saying sufficient precautions were taken to disinfect polling stations.

"It is important to vote in these times," President Emmanuel Macron said after washing his hands with sanitising gel and casting his ballot in northern France.

Prime Minister Edouard Philippe, who was also running for mayor of the Normandy port city of Le Havre, suggested on Saturday the election's second round on March 22 could be pushed back.

"The high abstention rate illustrates the growing worries of our fellow citizens about this crisis," Philippe said in a televised address, as estimates put him ahead in his mayor race.

But calling off the second round now would likely require a rerun of the first round as well, constitutional law experts say.

France recorded 36 more coronavirus deaths Sunday, the biggest one-day increase in the country since the outbreak, taking the total death toll to 127 deaths and 5,423 cases of infection since January, the national health agency said Sunday.

In polling stations across the country, people were visibly cautious, trying with difficulty to keep a safe distance from each other.

Poll clerks wore latex gloves, offered disinfectant and marked out lanes with arrows on the floor showing where people should stand while waiting for their turn. Some voters wore gloves and brought their own pens to sign off their vote.

Hours before polling stations opened, major opposition politicians, including the conservative heads of six regions, criticized the government for not calling off the vote.

France's municipal elections traditionally see a higher turnout, with local politicians often viewed in a better light than their national counterparts as they are considered more in touch with what's going on in people's everyday lives. 

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(With input from agencies)