The police believe the group may still be in the park, their statement said.
The kidnapped tourist was identified as Kimberley Sue Endecott, a 35-year-old United States citizen and one Jean Paul, a tour guide and driver attached to World Frontiers Safaris Uganda.
Security is always guaranteed by a network of Tourism Police, Uganda Wildlife Authority wardens as well as the military.
"The priority at this point is to locate, rescue and bring them back to safely".
Ugandan security forces were searching for them in an area close to the border with Democratic Republic of Congo.
Ms Namaye said security forces among other police, Internal Security Organisation (ISO), army and External Security Organisations (ESO) to trace for kidnapped tourists including Ugandans who went missing weeks ago.
He moved to Uganda in 1992 and joined the company with in 2007 with five years of experience in the tourism industry.
Rights groups who led the protests to the country's parliament in Kampala city, said more than 20 people, mostly women, and children, were abducted for ransom past year and called on the police to make these cases a priority.
Queen Elizabeth, in southwestern Uganda lies some 150 kilometres (90 miles) north of Bwindi Impenetrable National Park, famous among tourists for gorilla trekking. "We want to further reassure the public that this is the first incident of this kind registered in such a very peaceful setting".
In 1999, Rwandan rebels killed eight foreign tourists there, inflicting an enormous blow to Uganda's tourist industry.
The incident is believed to have happened between 6 and 7 pm Tuesday near a wilderness camp in Queen Elizabeth National Park, where two armed men held four tourists at gunpoint.
It borders its famous Virunga national park, Africa's oldest national park.
There are fears that the kidnappers could have crossed with the pair into the DR Congo.
Virunga suspended all tourism activities previous year following the kidnapping of two British tourists, Bethan Davies and Robert Jesty, in May 2018.
Subsequently, two people including an American national and the driver (Ugandan) of the van were taken by the yet to be identified people.