The move comes after Recep Tayyip Erdogan’s senior adviser suggested that the officers had been framed by the police and judiciary.
Hundreds of people were jailed in 2012 and 2013 in two high-profile cases, called Sledgehammer and Ergenekon.
Correspondents say the remarks represent a political turnaround.
“Our position on a retrial is a favorable one,” Recep Tayyip Erdogan told reporters in Istanbul on Sunday.
“First we must establish the legal grounding for fresh trials.”
It comes as political tensions run high over alleged corruption in the Turkish government.
Recep Tayyip Erdogan has accused the police and judiciary of orchestrating a probe which led to the resignation of his ministers.
The ruling AK Party is rooted in political Islam and has moved to curb the power of the Turkish military, which sees itself as guardian of the modern secular state founded by Mustafa Kemal Ataturk.
The prime minister now appears to have taken the side of the military he once opposed. In recent days, the army has filed a criminal complaint calling for retrials.
During the early years of his administration, Recep Tayyip Erdogan formed an unofficial alliance with prosecutors in an effort to remove the military from politics.
This effort culminated with two major trials relating to separate alleged plots – Sledgehammer and Ergenekon. They were seen as major challenges to Turkey’s secularist traditions.
But in December, some of the same prosecutors involved in those investigations ordered the arrest of a number of the prime minister’s own allies.
Three ministers resigned after their sons were arrested, along with dozens of others, over alleged wrongdoing in construction contracts and deals with Iran.
Recep Tayyip Erdogan condemned the investigation as a “dirty plot”.
The armed forces then suggested that this “plotting” also included the convictions of officers, and demanded a retrial.
The former armed forces chief, General Ilker Basbug, was among dozens of people given long jail terms. Lawyers, politicians and journalists were convicted, along with many military officers.
Analysts say the latest dispute over corruption is part of a power struggle between Recep Tayyip Erdogan’s government and an influential US-based Muslim cleric, Fethullah Gulen, who is said to have many followers within Turkey’s police and judiciary.
For decades, the armed forces were the ultimate arbiter in Turkish politics.
Between 1960 and 1997, the military forced out four civilian governments.
But over the last decade, Recep Tayyip Erdogan’s government has changed the balance of power in Turkey.
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