The breach occurred despite a recent purge of thousands of officials by Prime Minister Tayyip Erdogan, who accuses a covert network of enemies of sabotaging the state.
Foreign Minister Ahmet Davutoglu, in whose office the security meeting took place, said "everyone and everything within the Foreign Ministry will be investigated with utmost scrutiny" - a measure of the alarm stirred by the tape and fear that others might follow.
"This is an act of espionage against the security of the state, it is audacity the like of which we have never seen before," said President Abdullah Gul, an ally of Mr Erdogan.
The recorded meeting discussed whether to send forces across the Syrian border to secure the tomb of Suleyman Shah, grandfather of the founder of the Ottoman Empire.
Comments on the tape attributed to intelligence chief Hakan Fidan - one of Mr Erdogan's closest allies - suggested four men could be sent to Syria with eight rockets to fire on to empty land. This, the voice said, could be used to justify Turkish intervention.
Officials, aware that any involvement in Syria would be highly unpopular with Turkish voters, accept the tape is genuine but say it has been manipulated in places.