The co-leader of the far-right AfD (Alternative for Germany) has left the party less than 24 hours after its shock third-place result in the country's election.

Saying there was "disagreement over content", Frauke Petry told a news conference she would not sit with the AfD in the Bundestag (national parliament) but would instead serve as an independent MP.

She then left the room.

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Long considered to be one of the party's most recognisable faces, Ms Petry remained in the shadows of the election campaign after clashing with senior members.

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Leading AfD members Joerg Meuthen, Alexander Gauland and Alice Weidel said they did not know why she had left the meeting.

After winning 12.6% of the vote, the nationalist party will be the first hard-right, openly anti-immigration party to enter the German parliament since World War Two, with nearly 94 seats.

Image: Opponents of the Alternative for Germany (AfD) protest against election results

Angela Merkel's CDU/CSU alliance took 33% of the vote in the poll on Sunday, well ahead of the second-placed Social Democratic Party's 20.5%.

Despite Mrs Merkel winning her fourth term as expected, the rise of the AfD in a country sensitive to far-right politics has caused unrest on Germany's streets.

As the party celebrated its result in Berlin, at least 500 protesters gathered in the streets, with some shouting "all Berlin hates the AfD" and "Nazi pigs". Bottles were also thrown.

There were other protests in Cologne, Hamburg and Frankfurt.

German foreign minister Sigmar Gabriel equated the AfD party with the Nazis, as did Green co-leader Katrin Goering-Eckardt, who told supporters: "There will again be Nazis sitting in parliament."

The World Jewish Congress called the AfD "a disgraceful reactionary movement which recalls the worst of Germany's past".

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Founded in 2013 by an anti-euro group of academics, the AfD has links to the far-right French National Front and Britain's UKIP.

After exit poll results were announced, AfD co-leader Mr Gauland said the party would "change" the country, vowing to "hound" Mrs Merkel and "get our country and our people back".

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Image: Alexander Gauland vowed to change the country

French far-right leader Marine Le Pen congratulated the party, writing on Twitter: "Bravo to our allies from AfD for this historic score! It's a new symbol of the awakening of the peoples of Europe."

In her victory speech, Mrs Merkel vowed to win back voters from the AfD and admitted the party's entry into parliament poses "a big challenge".

After failing to secure a ruling majority, Mrs Merkel faces four years of government in a fragmented parliament.

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The complicated task of building a coalition with two new partners could now take several months.

Mrs Merkel told supporters in Berlin: "We are the strongest party, we have the mandate to build the next government - and there cannot be a coalition government built against us."

SPD deputy leader Manuela Schwesig has ruled out a re-run of Mrs Merkel's existing alliance with the party, confirming that her party will now go into opposition.

An alternative coalition for Mrs Merkel would be a three-way tie-up with the pro-business Free Democrats (FDP), who secured 10.7%, and the ecologist Greens, who achieved 8.9%.

Mrs Merkel said she was not planning to try to lead a minority government, stating: "I have the intention of achieving a stable government in Germany."

She has said she believes a coalition will be agreed by Christmas.