The flooding in parts of Bugisu, Mbale and Kapchorwa initially killed 10 people on Sunday, the state ministry in charge of relief, disaster preparedness and refugees in the Office of the Prime Minister said in a statement late on Sunday.
But the death toll rose further on Monday.
Uganda Red Cross spokesperson Irene Nakasita told reporters that so far rescuers had retrieved 21 bodies from Mbale and another three from Kapchorwa.
She said a truck carrying relief supplies was on its way to attend to those displaced in the affected areas.
The torrential rains come right after a prolonged drought in vast swaths of the country that has left many areas parched and crops in fields scorched.