Earlier, her spokesman Steffen Seibert dismissed the Nazi comparison as "absurd", but also said both sides should be "calm and level-headed" in managing their disagreements.
EU foreign ministers meeting in Brussels also urged restraint towards Turkey, though Austria and the Netherlands — also home to large ethnic Turkish populations — said they opposed campaigning by foreign politicians on their soil.
Asked whether the European Union should curtail funding aimed at preparing Turkey to join the bloc, Seibert said: "One will certainly have to continually ask the question, as the EU does with all of its spending, whether the payments are achieving the initially intended goal."
On Sunday Austrian Chancellor Christian Kern urged the EU to halt membership talks with Turkey and scrap or restrict 4.5 billion euros in pre-accession aid promised to Ankara by 2020.
Erdogan's comments have prompted shock and outrage among German politicians, and the leader of Germany's Turkish community said on Monday they could harm bilateral ties and further exacerbate tensions among Turks living in Germany.
"Erdogan went a step too far. Germany should not sink to his level," Gokay Sofuoglu, chairman of the Turkish Community in Germany, which groups 270 member organisations, told
Seibert told reporters Germany remained committed to good ties with Turkey because of their common interests, including the estimated 3 million people of Turkish background who live in Germany, NATO membership and the fight against Islamic State.
But he said Germany was continuing to press Turkey for fair treatment of the journalist Yucel and his speedy release. The Die Welt correspondent faces 10-1/2 years in prison if convicted
of charges of propaganda in support of a terrorist organisation and inciting public violence. Yucel denies the charges.
On Monday Taner Yildiz, chief adviser to Turkish Prime Minister Binali Yildirim, accused authorities in the town of Kelsterbach, west of Frankfurt, of cancelling a planned rally at which he had been due to speak.
"We reminded the (local) authorities that this was a democratic right," Yildiz told Reuters, adding that work to secure an alternative venue was underway.
German officials could not immediately be reached to confirm Yildiz's comments.
An estimated 1.5 million Turkish citizens living in Germany are eligible to vote in Erdogan's April 16 constitutional referendum.