They are seeking compensation of more than $5.5 million and an apology from Israel, Hurriyet Daily News reported.
Israeli forces killed the activists aboard the Mavi Marmara May 31, 2010.
The incident marked a low point in diplomatic relations between Israel and Turkey, observers said.
Turkey has Israel must apologize, compensate families of the victims and lift its naval blockade on the Gaza Strip to restore normal ties between the two countries.
Notable deaths of 2014 [PHOTOS]