Merkel's centre-right CDU party also did badly with 27.2 percent, compared to 38.3 percent last time round.

But the Greens (19.6%) and the far-right AfD party (13.2%) surged in support, with the AfD now entering regional parliaments in all 16 German states.

The ruling parties' poor outcome, which follows similar results in Bavaria earlier this month, meant the government had to agree a new "roadmap" or give up the ghost, an SPD spokeswoman said.

"We could then gauge the implementation of this roadmap at the agreed mid-term review, when we would be able to clearly see if this government is the right place for us," Andrea Nahles said.

"The message to the parties ruling in Berlin is: People want fewer disputes and more focus on the important issues," the CDU's Hesse state premier Volker Bouffier said.

His talk of "disputes" came after internal government disputes over how to treat migrants at the Austrian border and over the sacking of an anti-immigrant spy chief.

The SPD-CDU 'grand coalition' came together as Merkel's second choice after her talks failed with the Greens and the pro-business FDP parties following last year's inconclusive elections.

The surge in far-right support also comes amid criticism of her former open-door policy on immigration.

"The election was a success on all fronts," the AfD's Hesse leader, Joerg Meuthen, said.

But the Greens, who also did well in Bavaria, said the regional votes had shown that the CDU and its Bavarian sister party, the CSU, had been punished for trying to copy AfD rhetoric in a bid to poach far-right votes.

"People thought elections can only be won on the far right," Green party co-leader Robert Habeck said.

"Passion, optimism and pro-European politics can apparently also mobilise support," he added.