Reinhard Grindel said on Monday on Twitter via Associated Press: "football and the DFB stand for values that Mr Erdogan doesn't sufficiently observe".
Arsenal's Ozil and Manchester City midfielder Gundogan, who are both German internationals born in Gelsenkirchen and of Turkish origin, met Erdogan in London on Sunday alongside Everton striker Cenk Tosun. Therefore, it is not a good thing that our internationals have let themselves be exploited for his election campaign stunt.
Mr Erdogan condemned President Trump's decision to move the United States embassy to the contested city of Jerusalem, a move that Britain and other European powers oppose.
Chief US ally Britain reiterated its stated objection to the move, while the Iranian speaker of parliament said it showed that US President Donald Trump is "feebleminded" and "incapable of evaluating the long-term consequences of his actions".
Gündogan wrote: "For my honored President, with great respect".
It was one of a series of pointed criticisms Mr Erdogan made of the U.S., whose...
Gundogan, in a statement, said he, Ozil and Everton's Cenk Tosun, a Turkey worldwide, attended an event of the Turken Foundation, which assists Turkish students in the United States and the United Kingdom, and met Erdogan there.More news: Oil prices soar as USA exits Iran nuclear deal
More news: Former UFC star WATERBOARDS himself in freakish Donald Trump statement
More news: CM to announce Board exam results tomorrow
Asked about the photo, he added: "Our president Erdogan is visiting England and was an active footballer and he loves meeting Turkish football players especially, although he does meet foreign players in Turkey when he has the time".
Both players will be spoken to ahead of Germany's World Cup preparations.
"I don't think we should involve them, they are Turkish but are playing for another national team". Two hearts sometimes beat in players with an immigrant background.
Grindel also backed down from initial comments made on Monday, saying that one of the cornerstones of German football was integration rather than separation.
Gundogan insisted he "didn't want to make a political statement with this photo and even less so campaign for his election".
"We've always been clear that we want Turkey to uphold its global obligations, including respect for freedom of expression and political freedoms", he said. "It will be a lesson for them".