German Chancellor Angela Merkel has been re-elected for a fourth term while nationalists have made a historic surge in federal elections, BBC reported.

While her alliance has remained the largest party, it is the worst result for the alliance between the Christian Democrat (CDU) and the Christian Social Union (CSU) since 1949, when national elections were held in Germany for the first time after World War Two, it said.

Its current coalition partner, the social democratic SPD, says it will go into opposition after historic losses.

The nationalist AfD has won its first seats and is set to be the third party, a result that sparked some protests.

Dozens of demonstrators gathered outside the right-wing, anti-Islam party's headquarters in Berlin, some with placards saying "Refugees are welcome". Protests were also held in Frankfurt and Cologne.

Addressing supporters, Merkel, who has been in the job for 12 years, said she had hoped for a "better result". She added that she would listen to the "concerns, worries and anxieties" of voters of the Alternative for Germany (AfD) in order to win them back.

Merkel also said her government would have to deal with economic and security issues as well as addressing the root causes of migration - one of the main reasons behind the AfD's result.

"Today we can say that we now have a mandate to assume responsibility and we're going to assume this responsibility calmly, talking with our partners of course."