Berlin's Social Democratic Party top candidate Franziska Giffey attends a TV debate after local elections in Berlin. Reuters

The Social Democrats (SPD) won the regional election to lead the state government in Berlin, according to provisional results on Monday, meaning that their candidate Franziska Giffey will become the first female mayor of the German capital.

Germany's Social Democrats narrowly won on Sunday's national election and claimed a "clear mandate" to lead a government for the first time since 2005 and to end 16 years of conservative-led rule under Angela Merkel.

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Giffey, 43, who was previously family minister in Chancellor Angela Merkel’s national government, will take over from the SPD’s Michael Mueller as mayor after he decided not to run again.

Franziska Giffey takes to the stage at the election party of the Berlin SPD in Kreuzberg, Berlin, on Sunday AP

The centre-left Social Democrats (SPD) were on track for 26.0% of the vote, ahead of 24.5% for Merkel's CDU/CSU conservative bloc, projections for broadcaster ZDF showed, but both groups believed they could lead the next government.

The SPD looks set to continue their current coalition in city hall with the Greens and the Linke.

Giffey, once seen as a contender to lead the SPD on the national level, stepped down as minister in May after a scandal https://www.reuters.com/article/us-germany-politics-resignation-idUSKCN2D00Y2 surrounding plagarism in her doctoral thesis.