In a sign of heightened security, government forces set up three checkpoints on the Denton Bridge into the capital to search people as they headed into work and check identity papers, witnesses said.
The US government and the United Nations both issued statements condemning any attempts to seize power but also warning against any further violence.
There was no word from Jammeh in the aftermath of the turmoil but the president, who returned to the country overnight, was expected to make a traditional New Year's Eve speech later on Wednesday.
The capital was locked down by security forces on Tuesday after gunfire erupted early in the morning. The sole government statement so far has played down the incident, denying any instability.
Diplomats monitoring the country- one of the most secretive in the region- warned of the possibility of a crackdown on those accused of having links to the attack.
"There are fears of reprisals. It is about whether (Jammeh) can be seen to be calm and in control without it getting too bloody," said one Western diplomat.
The diplomat said four attackers were reported killed and four others injured in clashes. Most are believed to be former members of the Gambian military, the diplomat said.
Local media and several analysts said the assailants included Lamin Sanneh, a former head of the presidential guard, and a US Army reservist who had US-Gambian nationality.
Following brief talks at the UN Security Council, Secretary-General Ban Ki-moon called for a transparent investigation into the events and also urged restraint.
Jammeh's security forces foiled a coup plot in March 2006 and Amnesty International said in the wake of that incident it feared some of the alleged coup plotters may have been executed without trial.
Jammeh, 49, took power in a coup 20 years ago and since then has stifled dissent in his impoverished West African nation of 1.9 million.
He has faced increasing criticism from abroad over issues ranging from human rights to his claim he can cure AIDS.
This year the European Union withdrew millions of dollars in aid after Jammeh signed into law an act that could imprison homosexuals for life. The US government also recently removed Gambia from AGOA, its African duty-free trade partnership.
In 2012, Jammeh was criticised for suddenly executing nine people being held in prison.
The country attracts tourists, particularly during the northern hemisphere's winter. They include about 60,000 Britons a year. The British foreign office advised its citizens to stay indoors and avoid public gatherings.
Gambia's national territory comprises a splinter of land wedged into Senegal and facing the Atlantic. Senegalese police said on Wednesday Gambia's borders remained open.
© Thomson Reuters 2015