But Kahl also said he did not think the Turkish government was behind the coup.
There is a possibility that Turkish ministers could plan another rally in Germany ahead of an April 16 referendum on changing the constitution, President Tayyip Erdogan's spokesman said on Sunday, a move that could further heighten tension with Berlin.
More than 40,000 people have been killed since the PKK launched its insurgency against the Turkish state in 1984. "Turkey has tried on different levels to convince us of that fact, but they have not succeeded", foreign intelligence service chief Bruno Kahl told the German daily Der Spiegel.
The relations between the two countries have already been tense after various German states cancelled and banned political rallies of Turkish politicians before a referendum in Turkey that seeks to significantly expand presidential powers.
The PKK is listed as a "terrorist" organisation by the European Union and US.
"How can terrorist organization be allowed to gather in Germany, while government ministers of the Republic of Turkey are not allowed to meet with our citizens?" he asked at a rally in the southern Osmaniye province's Kadirli district.
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Britain's Prince William is taking flak for going on a ski holiday instead of attending a major royal engagement with his family. In an interview previous year , he said he was aware of the criticism and was willing to take on more royal duties.
In the interview with CNN Turk, Kalin also accused Germany of supporting the US-based cleric Fethullah Gulen, who Ankara believes was responsible for last year's attempted coup.
The Turkish foreign ministry said in a statement that Germany's toleration of a rally with symbols of a group that it itself regards as a terror outfit was the "worst example of double standards".
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.
Critics say the constitutional change would give Erdogan too much power.
Ankara blames Gulen's network of followers in the military for a failed coup attempt in July, when a group of rogue soldiers seized tanks, helicopters and war planes to attack parliament and attempt to overthrow the government.
Erdogan and the Turkish government want the United States to extradite Gulen, who denies involvement in the coup attempt.