German Chancellor Angela Merkel said on Sunday she wants the government coalition to continue despite the surprise announcement by Social Democratic Party (SPD) leader Andrea Nahles that she is to resign as head of the centre-left party.

"We will continue the work of government with all seriousness. And above all with a great sense of responsibility," Merkel said.

The issues that the government has to solve are still on the table - in Germany as well as in Europe and the rest of the world, she added. "And in this spirit we will continue to work."

Merkel's replacement as leader of the senior coalition party, the conservative Christian Democrats (CDU), Annegret Kramp-Karrenbauer appealed to the SPD, the junior partner in the coalition, not to endanger the stability of the government.

Kramp-Karrenbauer said she assumes that the SPD will quickly meet the necessary decisions to replace Nahles so that "the ability of the grand coalition to act is not affected."

"This is not the hour of tactical party considerations. We continue to stand by the grand coalition," she said, referring to the alliance between the CDU, its Bavarian sister party the CSU and the SPD that was formed after the 2017 general election.

The third coalition party also wants to stick with the current government arrangement. "We expect the SPD to contribute to Germany keeping a stable government," CSU head Markus Soeder told dpa on Sunday.

Nahles' move, ostensibly taking responsibility for her party's poor showing in last weekend's European elections, prompted questions about the future of Berlin's already shaky coalition government.

Nahles said she would formally declare her resignation as the SPD's first female leader to senior party figures on Monday.

"Discussions within the party parliamentary group and feedback from the party have showed me that the support necessary for me to carry out my offices is no longer there," Nahles said on Sunday.

The SPD garnered just 15.8 per cent of votes in the elections to the European Parliament, its worst-ever result in a nationwide poll.

The SPD leader said she would also give up her role as head of the party parliamentary group on Tuesday. She will give up her seat in the Bundestag at an undisclosed point in future, an SPD parliamentary spokeswoman told dpa.

The party decided on Sunday that Cologne Member of Parliament Rolf Muetzenich would be interim leader of the Bundestag party group, while Rhineland-Palatinate Premier Malu Dreyer has offered to temporarily lead the party.

Meanwhile, Finance Minister Olaf Scholz ruled out taking Nahles' place at the helm, even temporarily.

"No, I don't think that can be managed together with the office of finance minister," he said late Sunday on broadcaster ARD.

Scholz said there needed to be a sensible solution to the vacancy left by Nahles and that it would not be right for someone to try take all jobs for themself.

Voters appear to be punishing the SPD for re-entering a coalition with the CDU and CSU following the 2017 federal elections.

"Together we made a decision to take responsibility for our country as part of the government," Nahles said of the move, which was criticized by voices on the left of party, particularly its youth wing, who wanted to see the SPD go into opposition.

"At the same time, we are working on building the party back up and to convince citizens with new messages," Nahles added.

Many have blamed party infighting and public bickering for the SPD's plummeting popularity.

Berlin Mayor Michael Mueller called for a fundamental change to his party's policies following Nahles' announcement.

Nahles' coalition partners did have words of praise for the outgoing SPD leader on Sunday.

Kramp-Karrenbauer, who is also under fire after the CDU/CSU bloc also had a historically bad European election result, said her experience of Nahles in coalition negotiations and as SPD chair was "always as a strong, honest and reliable partner."

"I worked with her for many years, both as a federal minister for labour and social affairs, and as a party and group leader," Merkel said.

"I have always done it with confidence, and it has always been absolutely solid what we discussed with each other."

"She is a Social Democrat with heart and soul, you can say that. But I think she's also a fine character," Merkel said.

Meanwhile, a leader from the largest opposition party, the far-right Alternative for Germany (AfD), Joerg Meuthen, called for the whole government to step down.

"Who is still interested in whether someone like Andrea Nahles resigns and who follows her as the next political bankruptcy administrator of the former popular party the SPD?" Meuthen said on Sunday.

"The only one who has to step down in this country to clear the way for a real new beginning is Angela Merkel and with her the entire federal government."