Jammeh, who had been out of the country at the time of Tuesday's attack and has since returned to Banjul, the capital, alleged that the coup plotters had received backing from some foreign countries.
After hours of fighting, forces loyal to Jammeh's regime succeeded in getting the upper hand, killing five insurgents. It was not immediately known how many casualties were suffered by the national military.
"We are all gripped by fear," said a Banjul resident who spoke on condition of anonymity for fear of reprisals.
UN Secretary-General Ban Ki-moon has called for "a transparent investigation" into Tuesday's events that respects human rights, due process and the rule of law, UN spokesman Farhan Haq said.
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Jammeh is one of Africa's most vocal anti-gay leaders and has previously threatened to behead sexual minorities found in his country.
The US government recently removed Gambia from a trade agreement in response to human rights abuses, including a law signed in October that imposes life imprisonment for some homosexual acts.