Suspects have so far been arrested over the kidnap of American tourist Kimberly Sue Endicott and a tour guide, Jean Paul Mirenge- Remezo.
In a statement signed by Fred Enanga, the spokesperson of the Uganda Police, he noted: "the intelligence led operation which was calculated and tactical, in the early stages is now progressing unhindered, with raids and extensive searches in Kanungu district, where the suspects were arrested and the neighbouring areas."
The statement did not disclose the number of suspects.
Enanga said: "We want to applaud the joint security team, for ensuring the kidnapping incident, where the captors were armed, in a very dynamic setting, did not go wrong, and for their breakthrough in attempts to crack down, the criminal gang."
Kimberly and Mirenge was freed over the weekend in circumstances that are yet to be made clear.
While international media organisations quoted sources saying that a ransom had been paid for their release, Enanga told journalists that no money had been paid.
On April 8, the minister of State for Tourism Godfrey Kiwanda said the demands of the kidnappers had been met.
The kidnappers had asked for $500,000 (Shs 1.8 billion).