Without confirming the contents of the paper, Germany's interior ministry admitted that it made a mistake in transmitting the classified written response to a lawmaker without first consulting the foreign ministry.
The foreign ministry meanwhile rejected extracts of the response to a question from a Left party lawmaker, which was published by German public broadcaster ARD.
But Ankara demanded an explanation, blasting the document as a "new indicator of a warped mentality" targeting Turkey.
According to ARD, the document noted that "the numerous statements of solidarity and action of support for the Egyptian Muslim Brotherhood, Hamas and groups of armed Islamist opposition in Syria by the ruling party AKP and President [Recep Tayyip] Erdogan underline their ideological affinity to the Muslim Brothers".
"As a result of a gradual Islamisation domestic and foreign policy of Ankara since 2011, Turkey has developed into a central action platform for Islamist groups of the Near and Mid-East regions," it quoted the document as saying.
The EU and the US consider Hamas - which rules Gaza - to be a "terrorist" group.
In a bid to calm the row, interior ministry spokesman Johannes Dimroth stressed the importance of Turkey in fighting jihadist groups.
"We are deeply convinced that Turkey is the most important partner with regards to the fight against the so-called Islamic State group," he said.
Foreign ministry spokeswoman Sawsan Chebli also refused to confirm the contents of the document, but said: "On what has been published in the media, we do not share the assessment as a whole."
Relations between Germany and Turkey have been fraught, with ties frayed over the German parliament's decision to brand as genocide the World War I-era massacre of Armenians by Ottoman forces and also Ankara's threat to back out of a crucial March deal with the EU on migrants.
Berlin also angered Ankara by criticising Erdogan's post-coup crackdown, in which more than 35,000 people have been arrested.