"Five military officers have been arrested but the mastermind, defence chief Colonel Ndure Cham is on the run," said a statement from the presidential office.
"A group of army officers lead by Colonel Ndure Cham, chief of defence staff, were at an advanced stage in their plots to overthrow the constituted government of the Republic of The Gambia," said the statement.
"All those involved are presently under custody and helping the security forces in their investigation except the leader who is still at large," it added.
Mr Jammeh's office said the situation was under control in the tiny West African country which is due to hold presidential elections in October.
The president's office added there was "no cause for alarm" claiming "the situation is under control."
The statement came nearly 24 hours after Mr Jammeh cut short his working trip to Mauritania as the news of the alleged coup plot broke.
The Gambian capital Banjul was completely calm with no military presence visible, according to an AFP correspondent.
Earlier, police and military sources reported Colonel Cham had been arrested, along with four captains, one major and a civilian working in the country's civil aviation office.
Meanwhile Mr Jammeh has promoted Lang Tombong Tamba to the rank of full colonel and appointed him chief of staff.