Germany's centre-left opposition has won a thin victory over Chancellor Angela Merkel's coalition in a major state election, dealing her a setback as she seeks a third term later this year.

The opposition coalition of Social Democrats and Greens on Sunday won a single-seat majority in the state legislature in Lower Saxony, a region of 8 million people in northwestern Germany.

The state has been run for a decade by a coalition of Merkel's conservative Christian Democratic Union and the pro-market Free Democrats, the same parties that form the national government.

The 58-year-old Merkel will seek another four-year term in a national parliamentary election expected in September. She and her party are riding high in national polls, but the opposition hopes the Lower Saxony vote shows that she is vulnerable.