The Turkish Consulate General has inked a lease for new offices at Fisher Brothers’ 605 Third Avenue in Midtown East, according to the landlord. The consulate will decamp Durst Organization’s nearby 825 Third Avenue and move down the block to 19,871 square feet at 605 Third Avenue next month. The organization will take over the entire 30th floor of the 1.1-million-square-foot building between East 39th and East 40th Streets. Asking rent in the transaction was in the $70s per square foot. A Fisher Brothers spokeswoman declined to comment on the length of the lease.