BERLIN (Reuters) - Berlin on Monday rejected as "absurd" Turkish President Tayyip Erdogan's comparison of current German policies to the Nazi era, and said the European Union should check if funds aimed at preparing Turkey to enter the bloc were working as intended.

Government spokesman Steffen Seibert urged both sides to stay "calm and level-headed" and not lose sight of the close ties that bind the two NATO allies.

"We firmly reject any comparisons between the policies of the democratic Federal Republic of Germany and the Nazi times," he told a regular government news conference.

"Such comparisons are always absurd and out of place because they lead to only to one thing: a trivialization of crimes against humanity."

Erdogan on Sunday likened bans on political rallies by Turks in Germany to "fascist actions" during the Nazi era, further souring bilateral relations amid mounting outrage in Germany over Turkey's arrest of Turkish-German journalist Deniz Yucel.

Seibert said Germany would continue to allow Turkish politicians to speak in Germany about a referendum on expanding Erdogan's powers, as long as they were open about their intentions and did not import Turkish conflicts to Germany.

Asked whether growing differences between Turkey and Europe should prompt the EU to 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."

Separately, the leader of Germany's Turkish community said Erdogan's comments could harm bilateral ties and were exacerbating tensions among Turks 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 organizations, told Reuters, although he urged Berlin not to ban Erdogan from Germany.

Seibert's comments came after Austrian Chancellor Christian Kern on Sunday urged the EU to halt membership talks with Turkey and scrap or restrict 4.5 billion euros in pre-accession aid promised to Turkey until 2020.

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 Yucel and his speedy release. The Die Welt correspondent is facing 10-1/2 years in prison if convicted of charges of propaganda in support of a terrorist organization and inciting public violence.

Siebert conceded that the two countries had deep differences at the moment, but said the broader relationship remained essential.

"Let us talk open and critically with another, but let's not lose sight of the special importance of our close German-Turkish relations. Let's stay calm and level-headed," he said.

Two German towns last week canceled political rallies at which Turkish ministers had hoped to drum up support for a "Yes" vote in the April 16 referendum on expanding the president's powers. An estimated 1.5 million Turkish citizens living in Germany are eligible to vote in the poll, making them one of the largest constituencies outside Turkish cities like Istanbul.

German chancellor Angela Merkel insists the rallies were canceled by the local authorities for security reasons and that federal officials were not involved.

(Reporting by Joseph Nasr and Michael Nienaber; Writing by Andrea Shalal; Editing by Catherine Evans)