In a joint statement following the three-hour meeting on Thursday, the three men said: "The public must be assured that matters will be handled in line with the law and everyone should act responsibly not to damage institutions.''
The statement downplayed the importance of the rare trilateral meeting, saying the three of them had preferred to hold their routine meetings together this week.
The purported coup plot, codenamed "Operation Sledgehammer", was allegedly drawn up and discussed in 2003 within the Istanbul-based First Army, shortly after the Justice and Development (AK) party came to power.
It was not known whether the suspects made any move to activate the plan, first reported in January by the Taraf newspaper.
The arrests have fuelled political strains and unsettled financial markets in the country, adding to tensions generated by a clash between the ruling AK Party and the secularist army and judiciary.
The plot allegedly involved plans to bomb mosques and provoke tensions with Greece in a bid to force the downing of a Turkish jet, thus discrediting the government and leading to its downfall.
Speaking to Al Jazeera, Fadi Hakura, a Turkey specialist at the Royal Institute of International Affairs, said: "The facts are extremely murky, we really do not know whether this plan was a coup plot or not.
"The military claims that it was a simulation produced in 2003 for military training, whereas the government claims that it was a well-thought out coup plan to over throw the Islamic-rooted government.
"I would say that there is increasing concerns in some sections of Turkish society that perhaps the government may be pushing for a more confrontational attitude against the military to weaken its standing in public society.
"Because the military is the principle opponent at the present time to the Islamic-rooted Justice and Development party."
Other senior military officers have been indicted on charges of planning a separate plot by a far-right group known as "Ergenekon" to overthrow the government.
|The army has regarded itself as the guardian of a secular Turkish state [Reuters]
That trial is ongoing. Critics of the government say the Ergenekon case has been used to target political opponents.
The AK party, with its roots in political Islam, is accused by some nationalists of having secret plans to turn Turkey into an Islamic state.
The government rejects those claims, saying its intention is to modernise Turkey and move it closer to EU membership.
In 2008, the AK party narrowly escaped being banned for violating Turkey's secular system.
The armed forces have ousted four governments since 1960 and such an operation against them would have been unimaginable until recent years.