Angela Merkel on Monday called for calm as an escalating row threatened to destabilise relations with Turkey and jeopardise the EU’s controversial migrant deal.
A spokesman for Mrs Merkel said there was “absolutely no justification” for comments by Turkey’s President Recep Tayyip Erdogan at the weekend in which he accused Germany of “Nazi practices”.
Governments across Europe have condemned the Turkish president’s comments, in which he also threatened to “start an insurrection” in Germany.
Austria has called for an EU-wide ban on campaigning by Turkish politicians in the wake of the row.
But Mrs Merkel on Monday called for “cool heads to prevail”.
“Nazi comparisons are always absurd and out of place, because they only lead to trivialising of the Nazis’ crimes against humanity,” Steffen Seibert, the German chancellor’s spokesman said.
“To our Turkish partners, let us talk openly and critically, but let us remember the special meaning of our close relationship and let cool heads prevail.”
There are concerns the row could jeopardise the EU’s migrant deal with Turkey, which Mrs Merkel personally brokered.
The opposition Left Party on Monday called for Germany to unilaterally pull out of the deal in response to Mr Erdogan’s remarks.
The Turkish leader’s outburst came after local authorities in two German towns blocked appearances by Turkish ministers.
“Germany, you are not even close to democracy. Your behaviour is no different from the Nazi practices of the past,” Mr Erdogan said.
“I’ll come tomorrow if I want to, and if you do not let me in, or try to stop me speaking, I’ll start an insurrection.”
The ministers were campaigning ahead of a Turkish referendum next month in which Mr Erdogan is seeking extensive new powers.
Around 1.5m Turkish citizens living in Germany can vote in the referendum. Local authorities said they blocked the rallies because of concerns over crowding, but Turkey accused then of attempting to influence the outcome of the vote.
Mr Erdogan wants to address a rally in Germany later this month.
Austria has already said it will not allow any Turkish politicians to campaign on its territory, and on Sunday it called for an EU-wide ban in solidarity with Germany.
“A collective EU ban would make sense so individual countries like Germany don't end up being pressured by Turkey,” Christian Kern, the Austrian chancellor, told Welt newspaper.
There have been widespread calls in Germany for Mrs Merkel’s government to prevent Mr Erdogan campaigning in the wake of the arrest of a German journalist in Turkey.
Deniz Yücel, who holds dual German and Turkish nationality, was detained as part of a crackdown on media critical of Mr Erdogan, and is being held on charges of “spreading terrorist propaganda”.
Critics have accused Mrs Merkel of failing to stand up to Mr Erdogan for fear of endangering the migrant deal with Turkey, and she is under growing pressure over the issue.