The man who was killed had gone to help other tourists whose vessel had capsized in the Murchison Falls National Park, 230 kilometers (140 miles) northwest of the capital, Kampala, Ugandan army spokesman Lt. Chris Magezi said Tuesday.
After the river accident, they were driving in a vehicle when they came across two Lord's Resistance Army rebels, who "fired on the vehicle," instantly killing the British man, who had been driving, Magezi said.
Three tourists injured in the attack were being treated in Gulu Independent Hospital, in the main northern Uganda town of Gulu, he said.
The Lord's Resistance Army is fighting a 19-year insurgency in northern Uganda and in the past month its members have killed three aid workers, for the first time in the conflict.
Magezi said Tuesday's incident was not a deliberate strategy by the rebels to target tourists. The rebels "just bumped into the vehicle. The Ugandan army is in hot pursuit to get them, and we shall step up security in the park," he said.
The army commander in the Murchison Falls National Park area was arrested while the army investigates the incident, Magezi said.
In London, a British Foreign Office spokeswoman, without giving her name in accordance with British government policy, confirmed the death and said the tourists had been rafting from Egypt to the source of the Nile River. The tourists were from Britain and New Zealand, she said.
Sue McIntyre, whose husband had been on the expedition, told National Radio in New Zealand that the other tourists were "now safe."
She said her husband, Garth, had phoned her to say "he has got a gunshot wound to the head ... but it's not too major. He had stitches put in it, and said he's fine now." They had been on an expedition called the Ascent of the Nile, she said.
The British man who was killed had been called in to help them during the "most dangerous" part of the river trip, but he was not part of the expedition, she said, AP reports.