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Germany's Angela Merkel under threat from Pegida rallies

Anti-immigration and anti-Islam protesters took to the streets of Germany on Monday, and analysts warned they represented a "big challenge" to the country's Chancellor Angela Merkel and other European leaders.

Thousands of protesters marched in several German cities in rallies against higher levels of immigration in Germany, a country with some of Europe's most liberal border controls.

Pegida protesters in Dresden, January 5 2015
Robert Michael | AFP | Getty Images

Around 18,000 protesters gathered in the city of Dresden, according to Reuters, with similar demonstrations also held in Berlin and Cologne. The anti-immigrant rallies were organized by a grassroots movement called Pegida, or "Patriotic Europeans Against the Islamisation of the West," and are currently taking place most week in some German cities.

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The rallies come despite Merkel's New Year plea for Germans to shun such protests, in which she argued that "right-wing extremism, hostility towards foreigners and anti-Semitism should not be allowed any place in our society."

Rise of the right

Anti-immigration parties have seen their popularity rise throughout Europe over recent months, as the euro zone economy has struggled to recover and jobs remain scarce. However, the latest rallies in Germany show that the rise of such parties is not confined to countries with struggling economies.

European countries that are relatively economically prosperous – such as the U.K., Sweden and Germany – have also see the rise of populist anti-immigration, anti-EU parties such as the UK Independence Party (UKIP), the Sweden Democrats and the Alternative for Germany (AfD).

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Pawel Swidlicki, policy analyst at think tank Open Europe, told CNBC Tuesday that the Pegida movement in Germany was an "interesting development" that was linked to insecurity over the country's economy, which veered dangerously close to recession last year.

"There's a belief that this movement is a proxy for other general concerns such as competition for jobs and economic and cultural insecurity," Swidlicki added.

"We don't know what it's going to do or where it's going, but we're seeing the protests happen all over Germany, although it seems to be focused in the former East Germany, in cities like Dresden."

The weight of history

Germany is acutely sensitive to rallies of a right-wing nature following the persecution of Jews in the 1930s and 1940s under Nazi leader Adolf Hitler.

As such, the anti-immigrant protests have been met with resistance from anti-Pegida demonstrations in Berlin, Stuttgart, Cologne and Dresden, according to media reports -- with their number often outnumbering the right-wing protesters. Public buildings in Berlin and Cologne have also turned off their lights in solidarity with the counter-protests.

Still, the topic of immigration is hotly debated in Germany. The country has a population of around 80 million and around 20 percent – or 16.5 million -- of those are from a migrant background, according to the German Federal Statistical Office, Destatis.

Provisional results from the country's statistics body do indeed show that immigration is on the rise – one of the main complaints of the anti-immigration protestors. In 2013, 1,226,000 people immigrated to Germany -- an increase of 13 percent on 2012.

Merkel's 'biggest challenge'

Merkel heads a conservative-governing coalition made up of her party, the conservative Christian Democratic Union (CDU), and the Christian Social Union (CSU) party.

The Pegida phenomenon will be concerning Merkel, according to Open Europe's Swilicki, who said it was interesting to note that she had adopted a confrontational stance with the movement rather than trying to reach out to the protesters.

Alastair Newton, senior political analyst at Nomura, said the issue of immigration was the biggest challenge facing Merkel and other European leaders.

"I think we'll continue to see tensions over immigration, particularly in countries like Germany that are doing economically well… as Germany becomes more attractive, economically, to asylum seekers abroad," he said.

"The question is whether countries like Germany can absorb those people and turn them into productive, useful members of the economy – to the benefit not only of them but all of us as a society. That seems to me to be the big challenge facing European leaders today."

- By CNBC's Holly Ellyatt, follow her on Twitter @HollyEllyatt. Follow us on Twitter: @CNBCWorld