Turkey and the European Union - especially Germany with its large Turkish diaspora - are locked in a bitter dispute as tensions rise ahead of an April 16 referendum on expanding Erdogan's powers.
Erdogan made the remark about Merkel at the weekend after the authorities in Germany had refused to allow several Turkish ministers to campaign for a 'yes' vote on their soil.
"Nazi comparisons are unacceptable in any form," Merkel's spokeswoman Ulrike Demmer said Monday, adding that it was up to Turkey to tone down its rhetoric and avert damage to relations between the two countries.
She refrained from further comment, however, while a Foreign Ministry spokesman indicated that Berlin had no interest in entering a spiral of mutual provocations designed to boost support for Erdogan among Turkish overseas voters.
"Who would really benefit from it if we paid back in kind, if we answered using the same language as the Turkish president," said Martin Schaefer.
"It benefits mostly the Turkish president who... with threats, insults and more is seeking majorities of Turkish citizens in Turkey and also... in Germany for the constitutional referendum of April 16."
To hit back with strong verbal retaliation would mean falling for Erdogan's tactic, Schaefer said, stressing that Germany is "a strong, democratic country" that could handle such insults.
"We are not defenseless or stupid or naive and, if pushed too far, the government will react."
Merkel: Germany could ban Turkish campaign events
Merkel, herself, on Monday warned that Germany could ban future campaign events by Turkish politicians on its soil unless Ankara stopped "Nazi" jibes aimed at Berlin.
Merkel stressed that such insults must stop - "no ifs, no buts" - and that Germany reserved the right to "take all necessary measures, including reviewing the permissions" for campaign events it had already granted.
A stern-faced Merkel said that such comments were "breaking every taboo, without consideration for the suffering of those who were persecuted and murdered" by the Nazis.
Raising the issue at the start of a joint press conference with Japanese Prime Minister Shinzo Abe, she stressed that "appearances by Turkish politicians here can only take place on the basis of the principles of German constitutional law".