Various illegal groups from Somali Islamists to Congolese-based rebels sometimes operate in Uganda, but the kidnappers' identity was not known.
An elderly couple also at the scene were not taken and raised the alarm.
"I suspect the kidnappers left them because they were elderly. They took all their possessions," said Ugandan government spokesman Ofwono Opondo.
Califonia-based Endecott and the couple, whose relationship was unclear, entered Uganda on March 29 and flew the next day to the park in the country's southwest, the spokesman added.
The Somali Islamist militant group al Shabaab has carried out attacks in Uganda in the past, but has never been known to kidnap anyone for ransom there.
The park, Uganda's most visited, is located about 400 km southwest of the capital Kampala, near the border with the Democratic Republic of Congo (DRC), which is home to many fragmented rebel groups.
Police said the kidnapping appeared financially motivated, since the group quickly made a demand using Endecott's mobile.
"The joint security teams have cut off all exit areas on the border between Uganda and the DRC in search of the victims," the statement added, warning the group may still be in the park.
The US embassy in Kampala said it would be issuing a statement later.
In 1999, an American couple, four Britons and two New Zealanders were killed along with four Ugandan guides when their group was ambushed by gunmen in the Bwindi Impenetrable National Park. Survivors said the killers appeared to be Congo-based Hutu rebels.
Bwindi begins about 20 km south of Queen Elizabeth National Park, where tourists flock to see lions, hippos, crocodiles, chimpanzees and other African wildlife in an area of lakes, savannah, forests and swamps.
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