Sent by President Barack Obama at the end of 2011, the 100 American soldiers are sharing U.S. technology and experience.
The team is currently moving in on a remote central African village. The location is where three international armies have zeroed in on Kony.
For years, Kony has been wanted by the international criminal court for war crimes and crimes against humanity. An online campaign this year by the advocacy group Invisible Children made Kony a YouTube sensation.
Ugandan officials on Monday renewed a claim made over the years that the rebel leader and his Lord's Resistance Army are receiving backing from the government of Sudan.
Col. Felix Kulayigye, the military's spokesman, said some of the LRA rebels captured by the Ugandan military wore "new uniforms" supplied by Sudan, though military officials have not found LRA fighters with weapons supplied by Sudan.
The Associated Press contributed to this report.