* CDU slumps to historic defeats in two regional elections

* Setbacks follow slow national vaccine rollout

* Party also hurt by face mask procurement scandal

* Germany holds national election in September (Adds SPD's Scholz, Greens leader in Baden-Wuerttemberg)

By Paul Carrel

BERLIN, March 14 (Reuters) - Germany's Christian Democrats slumped to record defeats in two regional votes on Sunday after a muddled coronavirus response, dealing a setback to the party which faces federal elections in September without Chancellor Angela Merkel.

Merkel, in power since 2005, is not seeking re-election at the national vote and her Christian Democratic Union (CDU) is already missing the "Merkel bonus" she has brought them with four consecutive national election victories.

Anger over a face mask procurement scandal in the CDU is compounding frustration among Germans with Merkel's conservative-led coalition over a sluggish coronavirus vaccine rollout caused by supply shortages and excessive bureaucracy.

Voters used the state elections to vent their annoyance.

In the southwestern automotive hub of Baden-Wuerttemberg, the Greens won 31.4% of the vote and the CDU 23.4%, projections based on early results for broadcaster ZDF showed.

In neighbouring Rhineland-Palatinate, the left-leaning Social Democrats (SPD) came first again with 35.5% of the vote ahead of the CDU, which led there in opinion polls until last month but secured only 26.9% support in Sunday's election.

"This is not a good election evening for the CDU," a downbeat-looking Paul Ziemiak, the party's secretary general, told reporters after the exit poll results.

The ecologist Greens were jubilant.

"This is a super start to the super election year," said Robert Habeck, co-leader of the Greens, suggesting that the outcome boded well in a year which will culminate with the national election at which Merkel's successor will be chosen.

Along with fears of a potential third coronavirus wave, CDU officials worry the party's reputation took a hit in the last two weeks when several conservative lawmakers quit over allegations they received payments for arranging procurement deals.

The CDU has seen its national popularity wane from 40% last June, when Germany was widely praised for its response to the coronavirus pandemic, to around 33% this month.

The SPD's candidate for chancellor, Olaf Scholz, said Sunday's results showed a national government without the CDU and its Bavarian CSU sister party could be possible after September's vote. "A lot is possible," he told broadcaster ARD.