Turkey on Sunday also condemned a rally held in Frankfurt with banners and posters affiliated with the outlawed Kurdistan Workers' Party (PKK) on display.
"The fact that the head of German intelligence made such a statement will increase doubts about Germany and give rise to the question 'was German intelligence behind the coup?'" he said.
He said the demonstrators had used the upcoming Kurdish New Year festival of Newroz as a "pretext" for the rally as the new year only falls on Tuesday.
Turkey condemned the gathering as "unacceptable" and accused Germany of hypocrisy for allowing it.
About 300 people, vast majority of them civilians, were killed after rebel soldiers attempted to overthrow the government on July 15, bombing state buildings and killing civilians and security forces.
Some Turkish officials mooted the idea that Western powers could have been involved in the coup and Isik suggested Kahl's comment would raise questions about Germany's role.
He said the "scandal" of the Frankfurt demonstration showed that some European Union countries were actively working in favour of a "no" vote in the critical referendum.
President Tayyip Erdogan's spokesman said Kahl's comments were proof Germany was supporting Gulen's network, which Ankara refers to as the "Gulenist Terrorist Organisation" or "FETO".
Police in Frankfurt, where hundreds of officers were deployed to the event, described the protest as peaceful and said on Twitter that most of the demonstrators had complied with German laws, adding: "We want to guarantee they can exercise their fundamental rights". "Why are they protecting them?"
Kahl also said he did not think the Turkish government was behind the coup, saying: "The coup attempt was not initiated by the government".
Germany and Turkey have been locked in a deepening row after Berlin banned some Turkish ministers from speaking to rallies of expatriate Turks ahead of a referendum next month, citing public safety concerns.
Tensions are already running high between Berlin and Ankara after German authorities refused to allow some Turkish ministers to campaign in the country for a "yes" vote ahead of the April 16 referendum on handing Erdogan an executive presidency. The Turkish government says the changes would boost stability and make governance more efficient. More than 240 people died in the attempt.