The reason for the generals' resignations was not immediately clear, but tensions between the secularist military and the government of Prime Minister Tayyip Erdogan have run high in recent years.
However, CNN Turk also quoted the prime minister's office as saying the generals were not resigning but going into retirement. State-run Anatolian news agency reported Kosaner as resigning "as he saw it as necessary."
The Turkish lira weakened sharply on the news to 1.6964 against the dollar from an interbank close of 1.6805 on Friday.
The Supreme Military Council is due to hold a major meeting next week to discuss key appointments and President Abdullah Gul and Erdogan met Kosaner on Friday to discuss the matter.
Friction between the government and military has been fuelled by an ongoing trial targeting dozens of senior military officers accused of plotting to overthrow the government.
The "Sledgehammer" case, arising from an alleged coup plan presented at an army seminar in 2003, is one of several setting Turkey's secularist establishment against Erdogan's ruling AK party, which critics suspect of having a secret Islamist agenda. The AK party denies this.
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