German Chancellor Angela Merkel's Christian Democratic Union (CDU) party look to have suffered heavy losses in Sunday's regional election in Hesse state.

The CDU remained the largest party, but lost around 10 percentage points to score 28 per cent of the vote, public broadcaster ARD reported.

Meanwhile, junior federal government partners the Social Democrats (SPD) dropped almost 11 points to land on just 20 per cent.

The Greens came third and the far-right Alternative for Germany (AfD) entered the Hesse regional assembly for the first time with 12 percent of the vote.

In this June 18, 2018 photo German Chancellor Angela Merkel, left, talks with the Prime Minister of the Hesse state Volker Bouffier

The result means anti-immigration party AfD, which entered the federal parliament for the first time last year, is now also represented in all 16 German regional assemblies.

Volker Bouffier, the incumbent CDU state premier in Hesse and a Merkel ally, told supporters: 'We are in pain because of the losses but we also learnt that it is worth it to fight.

'The message to the parties ruling in Berlin is: People want fewer disputes and more focus on the important issues,' he said.

The Greens came third in the vote, narrowly losing out to junior federal coalition partners the SDP. Pictured is Hesse's Economy and Transport Minister of the Green party Tarek Al-Wazir

The CDU's poor result in Hesse, after its sister party in the state of Bavaria, the CSU, suffered its worst result there since 1950 two weeks ago, may turbo-charge a debate about who succeeds Merkel and when. She has been chancellor for 13 years.

The SPD fared even worse, winning just 20 percent of the vote in Hesse, down from 30.7 percent in 2013 and its worst result in the western state since 1946.

The party just managed to beat the Greens, who placed third with 19.5 percent.

The exit polls for ARD and ZDF public television gave Merkel's Christian Democratic Union up to 28 per cent support and the center-left Social Democrats 20 percent.

These results are significantly worse for the parties than the last time Hesse elected its state legislature in 2013.

Then, the CDU won 38.3 per cent of the vote and the Social Democrats won 30.7 per cent.

Thorsten Schaefer-Guembel, lead candidate of the German Social Democrats (SPD), and his wife Annette cast their ballots in Hesse state elections

The election has unusually high national political significance following months of infighting in Merkel's federal coalition.

The campaign in Hesse, which includes Germany's financial center of Frankfurt, has been largely overshadowed by the woes of a federal coalition that has been in office only since March. The state is home to 6.2 million of Germany's 82 million people.

Two weeks ago, two of the federal governing parties - the Christian Social Union, the Bavaria-only sister to Merkel's CDU, and the Social Democrats - were battered in a state election in neighboring Bavaria.

Merkel's chief of staff, Helge Braun, said that 'this is of course a difficult result for the CDU' but that his party remains the strongest in Hesse.

He said the national government must now pull together and 'show we are solving the problems that really move people.'

Following tensions and months of infighting in the federal coalition, the election has unusually high national political significance

The Social Democrats only reluctantly entered Merkel's national government in March, and many are said to be dismayed by what has happened since.

The Social Democrats' general secretary, Lars Klingbeil, said: 'This is a bad result for us, I can't put it any differently.

'This is a signal to the grand coalition that things must change. There will be an intensive discussion in the coming days.'

The result will prompt more fears about the government's stability. Merkel's fourth and probably final government has already come close to collapsing twice.

Reports claim that a growing number of SPD members feel their centre-left party is tarnished by its alliance with Merkel and would be better off rebuilding in opposition - a scenario SPD leader Andreas Nahles has resisted.

The ARD exit poll showed only 13 percent of CDU voters believed Merkel had helped the party in Hesse, down from 70 percent at the last state election in 2013.

The CDU holds its annual congress in December, when Merkel will seek re-election as party chairwoman.

She is likely to be reappointed but a weak show of support for her would undermine her authority and accelerate the succession debate.

Merkel's weakness at home could also have international consequences.

It may limit her capacity to lead in the European Union at a time when the bloc is dealing with Brexit, a budget crisis in Italy and the prospect of populist parties making gains at European parliament elections next May.