German Chancellor Olaf Scholz's Social Democrats narrowly beat the far-right AfD in a state election on Sunday in the formerly communist east, initial projections by public broadcasters said.

Scholz's centre-left SPD won around 31 percent against the anti-immigration, pro-Russian Alternative for Germany, which scored about 29 percent according to the projections.

The result in the state of Brandenburg offers a rare moment of respite for Scholz's embattled coalition government, which has sunk in opinion polls a year ahead of national elections.

The election in Brandenburg has been closely watched because Scholz's SPD has ruled there ever since Germany's 1990 reunification. The chancellor's own electoral district is in the state capital Potsdam, outside Berlin.

The AfD, which rails against asylum-seekers, multiculturalism, Islam and Scholz's government, had hoped to replicate its recent electoral success in the east.

Three weeks ago, it stunned the political establishment by winning its first-ever parliamentary vote – in the eastern state of Thuringia – and coming a close second in neighbouring Saxony.

Despite its ballot box success, the AfD is unlikely to take power in any state since all other mainstream parties have so far ruled out entering into a governing alliance with the party. (AFP)