France's far-right National Front (FN) has failed to win a single region in the second round of municipal elections, preliminary results show.

They indicate that the party has been beaten into third place, despite leading in six of 13 regions in the first round of voting.

Nicolas Sarkozy's centre-right Republicans are set to win most seats ahead of the ruling Socialists.

Acknowledging defeat, FN leader Marine Le Pen pledged to keep fighting.

And she blamed the outcome on the mainstream parties which joined forces to keep the FN from power, telling her supporters they had been "disenfranchised in the most indecent of ways by a campaign of lies and disinformation".

Marine Le Pen stood as a regional presidential candidate in the northern region of Nord-Pas-de-Calais-Picardie, while her niece Marion Marechal-Le Pen was the FN's candidate in the race in Provence-Alpes-Cote d'Azur, in the south.

After both led with more than 40% of the vote in the first round on 6 November, the Socialist candidates in those regions pulled out so their voters could support Republican candidates against the FN in the second round.

Marine Le Pen secured 42.2% of the vote in the second round in her region against the centre-right's 57.8%, French media report.

Marion Marechal-Le Pen took 45.2%, compared with 54.8% for her Republican rival.

Despite the defeat, the 26-year-old urged FN supporters to "redouble our efforts".

"There are some victories that shame the winners," she said.

Analysis: BBC's Hugh Schofield in Paris

There can be no hiding that the results of the elections are a big personal blow to Marine Le Pen.

She has lost the chance to govern a region and show the world that her party is serious. She has been reminded that however strongly the FN performs, the gates of power remain tightly closed.

But in a way that suits her fine.

Because what it all means is that nothing in France has changed. The two main parties continue sharing out the goodies (in this case deliberately conniving to keep hers as well).

Meanwhile unemployment rises; terror stalks; the grim insurrectionary mood continues to spread.

Marine's prospects for power may be limited, but her appeal is as strong as ever for France's growing numbers of disgruntled and disaffected.

That French "ouf" of relief? It's also the noise you make when you get a fist in the abdomen.

Xavier Bertrand, Republican regional presidential candidate in Nord-Pas-de-Calais-Picardie, said the French had given "a lesson of rallying together, courage. Here we stopped the progression of the National Front".

But Socialist Prime Minister Manuel Valls was less upbeat. He warned the "danger posed by the far right has not gone away, far from it".

And Mr Sarkozy said now was the time "for in-depth debates about what worries the French", noting security concerns, unemployment and frustration with the European Union.

These elections were to vote for councils and presidents of the 13 French regions, which have wide powers over local transport, education and economic development.

French media are predicting that the Republicans have taken seven regions and the Socialists five, with nationalists winning Corsica. Final official results are expected later on Monday.

One of the biggest upsets happened in the Paris region, Ile-de-France, which shifted from the Socialists to the Republicans for the first time in nearly 20 years.

The first round of voting on 6 December gave the FN the best election results in its history.

It was the first electoral test since the 13 November Paris attacks, in which 130 people were killed - an attack claimed by the so-called Islamic State group.

In the lead-up to the first round, opinion polls suggested that the popularity of the anti-immigration, anti-EU FN had increased since the deadly attacks.

The FN had been hoping a strong performance would boost Marine Le Pen's chances in the 2017 presidential election.