Rebels from Uganda's Lord's Resistance Army (LRA) shot dead a British tourist in an ambush in a northern Ugandan national park on the weekend.
A military source says a New Zealander and a Ugandan were abducted, but were rescued by troops.
On Saturday, suspected LRA rebels shot dead a British aid worker in an ambush in neighbouring southern Sudan.
The LRA has waged a 19-year-old war against the Ugandan government, and last month began targeting foreigners - apparently in reprisal for arrest warrants issued for their leaders by the International Criminal Court (ICC).
"This afternoon in Murchison Falls park, two LRA rebels killed a UK citizen," Lieutenant Chris Magezi, the army spokesman in northern Uganda, told Reuters by telephone.
He said a New Zealander and a Ugandan were also abducted by the rebels, but were later rescued by troops.
A British official in Uganda's capital Kampala confirmed reports of a Briton being killed by the rebels, but could not immediately provide more details.
Magezi said three other tourists - including another New Zealander and two other Britons - had fled into the bush but were later found safe by Ugandan soldiers.
He said the group had set out from Murchison's upmarket Paraa Safari Lodge to help whitewater rafters who had had an accident on the River Nile, which runs through the park.
As they returned to the lodge, he said, they ran into the rebels, who sprayed their car with bullets. One Briton died.
"Our troops are in hot pursuit of the rebels. Meanwhile, the lieutenant in charge of that area has been arrested for failing to provide security on the road," Magezi said.
In late October, two local aid workers were gunned down in northern Uganda, then an Iraqi and a Sudanese working for a Swiss-based mine-clearing agency were killed in an ambush on their convoy in southern Sudan where the LRA has bases.
Experts on the conflict say the rebels appear to changed tactics in response to an October 14 statement by the ICC saying it had issued its first arrest warrants for the LRA leadership.
Led by self-styled mystic Joseph Kony, the LRA insurgency has uprooted more than 1.6 million people in northern Uganda and triggered one of the world's worst humanitarian emergencies.
The cult-like group has never given a clear account of its political aims, but it is notorious for massacring civilians, mutilating survivors and kidnapping more than 20,000 children who are forced to serve as fighters, porters and sex slaves.
On Monday, Britain's Foreign Office said the LRA may now be targeting "white people", referring to a handwritten letter apparently written by the LRA and passed to locals last month.
has advised its nationals not to visit Murchison Falls following an
attack on a vehicle in the park in July.