Witnesses said the troops, who also set up checkpoints on roads leading out of the coastal city, were searching for suspects from Tuesday's assault on the presidential palace.
The attack, which was repelled by the security forces, took place while Jammeh was on a private visit to Dubai, diplomatic and military sources said.
"Gambian soldiers carrying guns are conducting a house-to-house," a woman living in Banjul told AFP, asking not to be identified. "They believe the attackers are still hiding in the capital."
A fisherman, who also requested anonymity because of the climate of fear in the city, said he had been warned by relatives not to head back with his catch to the usual dock outside Banjul because "members of the armed forces and the paramilitary are lying in ambush in the creeks at Denton bridge and Old Jeshwang".
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Military and government officials were not available for comment.
An intelligence services source said on Thursday that dozens of people had been arrested in connection with the pre-dawn attack, which was carried out by heavily armed men travelling by boat.