The German foreign ministry has demanded an explanation from the U.S. while opposition politicians accused have accused Mr Grenell of "interfering" in the country's politics.
Grenell referred to Kurz as a "rock star" in the interview, and explained, "I absolutely want to empower other conservatives throughout Europe, other leaders".
"I hope that Kurz's visit will lead Mr Grenell's tenure as ambassador in Germany to be short", added Schulz, playing on the German word for short - "kurz". "What this man is doing is unheard of in global diplomacy", Schulz told the German press agency DPA.
President Donald Trump's newly-appointed USA ambassador to Germany, Richard Grenell, has angered officials there by signaling that he aims to act as a spokesperson for right-wing policies promoted by Trump and other European leaders-prompting some to call for his expulsion from Germany less than a month into his new role.
Senior center-left MP and former European Parliament President Martin Schulz also chimed in, telling the German Press Agency that "Grenell does not behave like a diplomat, but like a far-right colonial officer".
Grenell, 51, had already caused a stir in May when he told German companies to "immediately" wind down their business in Iran following US President Donald Trump's decision to withdraw from the 2015 Iran nuclear deal.
The comments drew a furious response from many Europeans and prompted the German Foreign Ministry to request a clarification of his remarks.
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"They're representatives of the White House, whether it's this administration or other administrations, and we hear them voicing their opinions", she said. And there are sometimes opinions that people may or may not like. "And there is the right to free speech as well". "We obviously have a very long history with the government of Germany, and we have a strong relationship with the government of Germany".
"We're not supporting any political party".
Sahra Wagenknecht, the leader in parliament of Germany's opposition Left Party, was less diplomatic than the governing party politicians, calling for Grenell to be removed.
Despite being smeared both in the Washington Post and the Huffington Post by anti-Trump columnists, Grenell appeared to be totally unapologetic regarding his comments, going as far as returning the favor and calling out the media.
Grenell had certainly fulfilled his task if he was sent to Germany to destabilise Merkel's coalition or the Atlantic alliance, she said, "but if those are not his orders. then a different set of questions has to be asked". "For that matter, why is he an American ambassador at all?"
Richard Grenell's controversial statements sent waves across Berlin when the United States ambassador told Breitbart that he is overjoyed by the "European groundswell of conservative policies" that has come about because of the "failed policies of the left".