He said talks with the German president and German Chancellor Angela Merkel were fruitful.
Relations between the two countries started to deteriorate after US Evangelical Pastor Andrew Brunson was jailed in 2016 for his alleged ties to the movement founded by Fethullah Gulen, which is considered a terrorist organization by Ankara.
Turkish President Recep Tayyip Erdogan addresses a session of the parliament in Ankara on October 1, 2018.More news: Ronaldo threatens to sue over 2009 rape allegations
A number of dual German-Turkish citizens have been imprisoned in the ensuing crackdown against the coup's alleged plotters, with Berlin insisting on their immediate release.
Erdogan said that the U.S. administration tried to solve issues between the two countries "with the language of threat instead of dialogue".
While a resumption of accession negotiations for Turkey's moribund EU bid was not on the table, some improvements - such as a modernisation of a Customs Union - could take place after European parliament elections in May 2019, said Mr Toygur.
In its more than 30-year terror campaign against Turkey, the PKK - listed as a terrorist organisation by Turkey, the USA and the European Union - has been responsible for the death of some 40,000 people, including women and children.More news: Valencia look to extend Manchester United's poor run
Erdogan is due to open a mosque which was built by a group with ties to Turkey in the city on Saturday.
Mr Steinmeier said the "strong emotions" the visit aroused in Germany were a reflection of tensions that have yet to be overcome and warned: "A single visit is not enough to restore normality". The economic strain has been one of the major issues in the capital of Ankara.
Many waved Turkey's red and white flag or held up pictures of Erdogan, with crowds cheerfully breaking into regular chants of the president's name or shouting "Who is the greatest?"
But he expressed satisfaction that "both sides made a cautious attempt at rapprochement".More news: New NAFTA deal could have impact on regional auto industry