Ugandan police had said on April 4 that an armed gang kidnapped Kimberly Sue Endicott and her tour guide at gunpoint from the national park and had made frequent demands for a $500,000 ransom.
The official said he did not know the identity of the kidnappers and that Wild Frontiers paid the ransom.
An elite army unit is searching the area, the border to Congo is closed, and the Federal Bureau of Investigation is actively a part of the negotiations with the kidnappers demanding US$500,000.
It will be remembered that the kidnappers using the Kimberly's phone had demanded for a ransom of United States dollars 500,000 (about Shs 1.8 billion).
It remains unclear if a ransom was paid in the case of Endicott, who is from Costa Mesa, California, where she has a small skin care shop.
"Bring them to justice openly and quickly!", Mr Trump tweeted just hours after President Yoweri Museveni tweeted insisting Uganda was safe for travellers and vowed to strengthen security in national parks.
The Ugandan police said in a statement posted on Twitter Sunday that the police and security forces "have rescued" the two kidnapping victims.
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Joint security teams cut off all exit areas on the border between Uganda and Congo to search for Endicott and the tour guide.
An American who was kidnapped along with her driver in Uganda last week has been recovered unharmed, a spokesman for the Ugandan government said Sunday. Police had said they would not offer the money.
Soldiers have fanned out along the porous border with the Democratic Republic of Congo, with security forces insisting they believe the pair remain in the country.
"God bless them and their families", Trump said on Twitter.
Bashir Hangi, the spokesperson for the Uganda Wildlife Authority, acknowledged the kidnapping could hurt the tourism industry but said tourists need to be cautious when traveling in national parks.
Secretary of State Mike Pompeo had said at a Tuesday event for families of US citizens held captive overseas that he understands some people want to do anything to get their loved ones back but paying ransom would just lead to more kidnappings.