Egyptian President Mohamed Mursi, an Islamist elected in June, has sought to deepen ties with Turkey and this month addressed the conference of the ruling Turkish Justice and Development (AK) Party.
Turkey was one of the first countries to speak out in support of the Egyptian uprising which toppled Hosni Mubarak and led to the Muslim Brotherhood winning power.
The annual drill, which is called Sea of Friendship and began on Sunday, is one of several such joint military manoeuvres between Egypt and Turkey.
The official, who asked not to be identified, said it involved five Egyptian navy units and the Egyptian air force.
The official also said Egypt would hold the "Bright Star" joint exercise with the US military in the second half of 2013. The drill, held every two years, was cancelled in 2011 because of the political turmoil in Egypt. It is seen as a cornerstone of U.S.-Egyptian military relations.
In 2009, the exercise also included forces from Jordan, Kuwait, Pakistan, Saudi Arabia and Turkey.