The authorities did not immediately confirm reports by NBS Television and other local media of an explosion near the Munyonyo Martyrs Shrine.
But army spokesman Chris Magezi posted on X that a "counter-terrorism unit this morning intercepted and neutralized two armed terrorists in Munyonyo, an upscale city suburb".
He said security services were on "heightened alert to ensure the Martyrs Day celebrations proceed without disruption".
Uganda marks Martyrs Day each June 3 to remember the killing of 45 Christian converts in the 1880s on the orders of Mwanga II, king of Buganda, which later became part of Uganda.
The event draws huge numbers of pilgrims from across east Africa and beyond.
Uganda, ruled by President Yoweri Museveni for almost 40 years, has faced persistent threats and attacks over the years from an array of actors, including some linked to the Islamic State group.
er/jhb
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