Abdullah Gul made the statement after a summit with PM Recep Tayyip Erdogan and armed forces chief Gen Ilker Basbug.
Tension between the government and the military has risen following a round of arrests over the alleged plot.
The former heads of the navy and air force were freed having been questioned over the coup plot, reports said.
It was unclear whether the two men - arrested on Monday with more than 40 other officers - face charges, Anatolia news agency reported.
Some 20 senior military officers have been charged and remanded in custody this week over the suspected 2003 plot.
The military has denied any coup plot and has held its own officers' summit to discuss the "serious situation" in the wake of the latest arrests.