Kabwegyere said the government had deployed a rescue team on the ground with aid and the Red Cross had dispatched a team of doctors.
Police and volunteers have joined the effort of rescuing people from buried homes, he added.
Malcolm Webb, a journalist in Uganda, said the rescue operation was complicated as many roads had been destroyed and further rain made the working conditions more difficult.
"The closest place where people can get healthcare is two hours away. Even there conditions are fairly basic," he told Al Jazeera.
"The hospital doesn't have film to X-ray patients with broken bones and have to send them on to the next town."
Parts of Uganda and neighbouring Kenya have had unusually high rainfall over the past two months, which normally is a dry period between rainy seasons.
Kabwegyere warned that "landslides are expected to continue as the rains intensify in the region".