Chancellor Angela Merkel's Christian Democratic Union (CDU) has won the regional elections in Germany’s most populous state, exit polls suggest, boosting its hopes of retaining power in September's national vote.

The Social Democrats (SPD) conceded defeat in Sunday's vote in North Rhine-Westphalia (NRW), and their regional chairman, Hannelore Kraft, resigned.

The CDU won around 34 percent, up from 26.3 percent in 2012, according to an exit poll on public broadcaster ARD just after polls closed.

The SPD, which has ruled NRW for most of the past half century, fell to around 30 percent from 39.1 percent.

"This is a great day for North Rhine-Westphalia," said local CDU leader Armin Laschet, who will most likely become state premier.

"We accomplished our two goals: defeating the SPD-Greens coalition and becoming the strongest party in the state."

Kraft said she took "personal responsibility for this defeat" before announcing her decision to step down.

SPD deputy chief Ralf Stegner called it a "very dark day for the SPD" but said the game is not over.

"The boxer SPD has received a serious punch but is still standing," he said.

The Free Democratic Party (FDP), Germany's liberals, fared significantly better with around 12 percent of the votes and are already claiming a comeback on the national political stage, according to its chairman Christian Lindner.

Why this regional election matters?

NRW is Germany's most populous state with a fifth of the country's voters living here.

The regional results are a fair indication of things to come in September's general election where Merkel would be seeking re-election for a fourth mandate.

Merkel is already the longest-serving chancellor in Germany and the longest-serving country leader in post-war Europe.

In 1995, the region came under the rule of a coalition of SPD and SPD-Greens which then managed to seize the popular vote from Chancellor Helmut Kohl, the prime figure of Germany’s reunification.

In 2005, the conservatives were elected into power in NRW before going on to take Berlin as well.

Social democrats have ruled this region since 1966 with only one five-year-exception. Seen as a traditional centre-left stronghold, Sunday's result means chances for Schulz to become chancellor in September are now getting smaller.

Who is going to rule this region?

According to the projection figures, no party can claim an absolute majority.

In this respect, NRW is also a peculiar case in German politics, where coalition options are well defined beforehand.

The FDP have opted out of a coalition with the SPD and the SPD-Greens who do not want to form a government with the Conservatives and the Liberals.

The SPD has rejected the option of ruling with the Greens and the Left, a party that has also been rejected as partners by the Conservatives.

No one wants to talk to the right-wing populists.

The reasonable scenario at this point would be a Big Coalition where the Conservatives would have the SPD as a junior partner.

That has already happened twice on national level in Germany - the current Merkel cabinet is made up of this partnership. However, a Big Coalition would be a first in NRW.

The other possibility would be a Conservative-Liberal coalition if the Left does not manage to pass the five percent hurdle and make it into the regional parliament.