Angela Merkel has pledged to listen to the concerns of people who voted for the far-right AfD party in a bid to win back their support.

In a victory address following initial results that saw her returned for a fourth term as Chancellor, Ms Merkel spoke of "illicit migration" and "internal security" – two areas the AfD has made inroads.

The CDU party leader said she would solve the "problems" – and also address the "fears" – of people who voted voted for the far-right.

The AfD – Alternative for Germany – won around 13 per cent of the vote, according to election-night projections. While Ms Merkel's CDU party won the most votes it was down on 2013 levels.

"We got where we wanted to be, we wanted to be the strongest power. It is down to us to form a government, and against us, no government can be formed," she told CDU supporters assembled an election night party in Berlin.

"After 12 years of being responsible for the government, the result we had today is really not something you can take for granted. Naturally, there's a challenge facing us for the future, and that is that the AfD has made it into parliament.

"We will have to win back those who voted for the AfD by solving their problems, by taking on board their concerns – their fears in some cases – but also by demonstrating good policymaking.

"In recent months we have fought for a Germany that we want to live in well, and now we need to set the course to ensure that in five and ten years' time it's still the case."

Though popular in Germany, Ms Merkel has faced some criticism from the right for her commitment to helping and taking in large numbers of refugees.

German election 2017 Show all 14 1 /14 German election 2017 German election 2017 German Chancellor Angela Merkel (R) poses for a selfie with a boy before addressing an election campaign rally of the Christian Democratic Union (CDU) in Kappeln Odd Andersen/AFP German election 2017 German Social Democrat (SPD) and chancellor candidate Martin Schulz speaks during an election campaign stop on September 20, 2017 in Gelsenkirchen. Schulz trails Chancellor and Christian Democrat (CDU) Angela Merkel by double digits Sascha Schuermann/Getty Images German election 2017 Sahra Wagenknecht, top candidate of the left-wing Die Linke party for upcoming general elections, gives a speech during a session at the Bundestag (lower house of parliament) in Berlin on September 5 John MacDougall/AFP German election 2017 Top candidate for the Greens for the 2017 German federal elections, Cem Ozdemir, speaks during an election campaign rally of the Alliance '90/Greens in Stuttgart, southern Germany on September 20, 2017, during the final days before Germans head to the polls Thomas Kienzle/AFP German election 2017 Leader of the Free Democrats (FDP) and main candidate in the upcoming parliamentary elections, Christian Lindner gives a speech during the party congress in Berlin on September 17 Odd Andersen/AFP German election 2017 Alice Weidel and Alexander Gauland, co-lead candidates of the right-wing, populist Alternative for Germany (AfD) political party, speaking to the media on Islam, immigration and crime next to an AfD poster that reads: 'Crime Through Immigration, The Refugee Wave Leaves Behind Clues!' on September 18, in Berlin Tobias Schwarz/AFP German election 2017 People listen to German Chancellor and Christian Democrat (CDU) Angela Merkel speak at an election campaign stop on September 19, 2017 in Schwerin Getty German election 2017 Refugees from Syria prior to the arrival of German Chancellor and Christian Democrat (CDU) Angela Merkel at an election campaign stop on September 19, 2017 in Schwerin Sean Gallup/Getty Images German election 2017 The audience cheers whilst listening to German Social Democrat (SPD) and chancellor candidate Martin Schulz speaking during an election campaign stop on September 14 in Munich Joerg Koch/Getty Images German election 2017 German Chancellor Angela Merkel holds up a tomato as she addresses an election campaign rally of the Christian Democratic Union (CDU) in Lingen on September 13 AFP/Getty Images German election 2017 Alexander Gauland, top candidate of Germany's anti-Islam, anti-immigration AfD (Alternative fuer Deutschland) party for upcoming general elections, walks past supporters as he attends an election campaign event in Nuremberg Daniel Karmann/AFP German election 2017 British politician and former UKIP leader Nigel Farage speaks at an event held by the German right-wing, populist Alternative for Germany (AfD) political party as AfD leading member Beatrix von Storch looks on on September 8, 2017 in Berlin Sean Gallup/Getty Images German election 2017 Martin Schulz (C), chancellor candidate of the German Social Democrats (SPD), looks on in a fest tent at the Gillamoos amusement fair on September 4, 2017 in Abensberg, Germany. Politicians, among them elections candidates, from Germany's major political parties are attending the fair today in what is an an annual tradition Johannes Simon/Getty Images German election 2017 An Alternative for Germany (AfD) campaign poster is vandalised in Berlin. Germans go to the polls on September 24th, with the AfD widely expected to garner enough votes to enter the federal parliament. Campaign poster reads: 'New Germans? we'll make them ourselves.' AFP

At this year's elections, the AfD ran an explicitly anti-Islam campaign, arguing that "Islam is not a part of Germany".