Police blamed the attack on Allied Democratic Forces, accused of slaughtering thousands of civilians in the violence-ravaged eastern DRC.
Uganda said on October 18 that it was hunting down gunmen who killed a honeymooning couple and their safari guide in one of the country's famed national parks in an attack claimed by the Islamic State group.
President Yoweri Museveni condemned what he described as a "cowardly act" and vowed the assailants would pay with their lives.
Police said a Briton and a South African were killed along with their Ugandan guide in Tuesday's attack and blamed an IS-linked armed militia based in the neighbouring Democratic Republic of Congo (DRC).
The Islamic State claimed responsibility in a statement released on Wednesday, saying the attackers had killed "three Christian tourists... one of them a Briton" with machine guns.
The trio were targeted by the attackers in Queen Elizabeth National Park in Southwestern Uganda and their vehicle set ablaze, police and park officials said.
"It was a cowardly act on the part of the terrorists attacking innocent civilians and tragic for the couple who were newlyweds and visiting Uganda on their honeymoon," Museveni said on X, formerly Twitter.
"Of course, these terrorists will pay with their own wretched lives."
Police blamed the attack on the IS-affiliated Allied Democratic Forces (ADF) that is accused of slaughtering thousands of civilians in the violence-ravaged eastern DRC.
A South African official said consular authorities were in touch with the family of the South African national killed in the attack.
"We would also like to join the international community in condemning this terrorist attack. Terrorism in whatever shape or form has no place in our society," South Africa's foreign ministry spokesman, Clayson Monyela, told AFP.
Ugandan military spokesman Felix Kulayigye said a joint army, police and wildlife authority force "has deployed all resources, both technical and physical, in pursuit of these terrorists and will ensure they account for their heinous acts".
Britain issued a warning to citizens against travelling to the park while France also told its nationals to be prudent.
Kulayigye urged the population "to be vigilant and cooperate with our forces" but also sought to assure tourists it was an "isolated incident" and Uganda remained a safe country.
The popular park is rich in wildlife across its 700 square miles (1,800 square kilometres), including lions with an unusual ability to climb trees.
Museveni called on Uganda's army and other security forces to ensure "these mistakes do not happen again and that the ADF is wiped out".
"The terrorists will be defeated", he added.
Tuesday's attack came after Museveni said Sunday that police had foiled an ADF bomb plot on churches 50 kilometres (30 miles) from the capital Kampala.
Earlier that day, the veteran leader also said Ugandan forces had carried out a series of air strikes against ADF positions in DRC and claimed a number of militants were killed.
Queen Elizabeth Park shares a border with DRC and its renowned Virunga National Park, a habitat for rare mountain gorillas, and where armed groups are believed to operate.
In 2019, a US tourist and her safari guide were kidnapped by four gunmen during an evening game drive through the Ugandan park. They were recovered unharmed after a ransom was paid.
The ADF is historically a Ugandan rebel coalition whose biggest group comprised Muslims opposed to Museveni.
Established in eastern DRC in 1995, the group became the deadliest of scores of outlawed forces in the deeply troubled region.
It has been blamed for massacres, kidnappings and looting, with a death toll estimated in the thousands.
In June, ADF fighters were blamed for killing 42 people including 37 students at a high school in western Uganda close to the DRC border in the worst such attack in the country in more than a decade.
Tourism is a top foreign exchange earner in Uganda, contributing almost 10 percent of gross domestic product (GDP) last year, according to government figures.