Paris Mayor Anne Hidalgo declared victory in her reelection bid as municipal elections postponed by the coronavirus crisis have seen a strong breakthrough from the greens across the country.

Sunday's voting also appears as a setback for French President Emmanuel Macron's young centrist party, which was fielding municipal candidates for the first time and still lacks local roots across France.

Hidalgo, a Socialist, largely beat conservative candidate Rachida Dati, according to estimates based on partial results. She was first elected as Paris mayor in 2014. Her reelection will allow her to oversee the 2024 Summer Olympics.

Hidalgo is backed by the Europe Ecology-The Greens party, which gained strong influence nationwide.

Paris Mayor Anne Hidalgo gesturing after her victorious second round of the municipal election Sunday. (AP Photo/Christophe Ena)

Green candidates won in France's major cities including Marseille, Lyon, Strasbourg and Bordeaux, often taking the lead in their alliance with the weakened Socialist Party.

The second round of the municipal elections has seen a record low turnout amid lingering worries about the pandemic.

Only 40 percent of voters cast ballots as people were required to wear masks in polling stations, maintain social distancing while in lines and carry their own pens to sign voting registers.

Poll organizers were wearing masks and gloves for protection, and in some places they were separated from voters by transparent plastic shields. Mail-in voting isn't allowed in France.

Macron expressed his "concerns" over the low turnout, "which is not very good news," according to his office.

Paris Mayor Anne Hidalgo getting a bouquet of flowers after her victorious second round of the municipal election Sunday. (AP Photo/Christophe Ena)

Interior Minister Christophe Castaner, in charge of organizing the elections, said that "everywhere across France, health measures ... were able to be respected. That is a satisfaction."

Sunday's voting was meant to choose mayors and municipal councilors in about 5,000 towns and cities.

The electoral process was suspended after the first round of the nationwide municipal elections on March 15, which produced decisive outcomes in 30,000 mostly small communes. Macron's critics say he shouldn't have allowed the first round to go ahead at all, since it was held just as infections were exploding across Europe and just two days before France introduced sweeping nationwide lockdown measures.

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The spread of the coronavirus has slowed significantly in France in recent weeks and almost all restrictions on social and business activity have been gradually lifted over the last month. France has reported nearly 200,000 confirmed cases and 29,781 deaths in the pandemic but experts believe all reported figures are undercounts due to limited testing and missed mild cases.

The elections, though ostensibly focused on local concerns, are also seen as a key political indicator ahead of the 2022 French presidential election.

Macron had said he wasn't considering the elections as a pro- or anti-government vote.

Yet a government reshuffle is expected in the coming weeks, as Macron seeks a new political boost amid the economic difficulties prompted by the virus crisis. French authorities have faced criticism during the pandemic over mask shortages, testing capacity and for going ahead with the first round of elections instead of imposing a lockdown earlier.

Prime Minister Edouard Philippe, whose job may be threatened by the reshuffle, won a large victory in his hometown of Le Havre where he was running for mayor.

Philippe has seen his popularity increase significantly in recent weeks. He may appoint someone else to act as mayor if he remains at the head of the government.

Recent opinion polls show Macron's popularity rating is hovering around 40 percent, which is higher than from before the virus outbreak.

His party, Republic on the Move, didn't have candidates in every race and in some instances was backing local politicians from the left or the right instead.

Government spokesperson Sibeth Ndiaye acknowledged the party's modest result in the elections, stressing that planting local roots "is taking time."

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The conservative Republicans party, which was the big winner in the 2014 municipal election and has a strong network of local elected officials, appeared to do well again.

The anti-immigration, far-right National Rally won a symbolic victory in the southern city of Perpignan, leading Louis Aliot to become the first member of the party to run a city of more than 100,000 inhabitants.