The animals were first spotted on Tuesday, a spokeswoman for the park, in Australia’s Northern Territory (NT), told CNN in a statement.
Since then, park staff have been closely monitoring one whale, which appears to be stuck. The spokeswoman said the other two are thought to have left the area, though rangers cannot be completely certain.
While scientists can’t say for sure what happened, they believe a “wrong turn” is the most likely explanation, the spokeswoman said.
“As far as we’re aware, this is the first time this has happened,” it said.
“We are monitoring the situation and working with NT government authorities to gather data on this unusual event, and an expert working group has been set up to monitor the whale and prepare plans for intervention if required.
“The last thing we want is a collision between a boat and whale in waters where crocodiles are prevalent and visibility underwater is zero. We also don’t want boats to inadvertently force the whale further up the river.
“The whale is not in distress at the moment and it is not an emergency situation. The best case scenario is for the whale to make its way back out to sea.
“Kakadu National Park and NT Government scientists will continue to monitor the whale in the coming days. We appreciate that this is a very unusual and exciting event, however, our priority at present is to ensure the safety and wellbeing of visitors and the whale.”
Most bodies of water within the park are inhabited by saltwater crocodiles, which are ambush predators that have been known to attack and kill humans. Despite their name, they can also be found more than 100 miles up river from the coast in freshwater habitats.
According to the park’s guidelines to visitors, the crocodiles can stay hidden under water for long periods and can move with great stealth and camouflage. They are quick-acting and have been known to move at speeds of up to 40 feet per second.
Earlier Monday, park staff met with experts to discuss how best to help the whale if necessary.
Carol Palmer, senior scientist in the NT government, said: “The Northern Territory Government is working closely with staff and traditional owners at Kakadu National Park, plus other very experienced experts, to ensure we give the whale the best chance of getting back out to sea.”
Feach Moyle, head of Kakadu’s country and culture section, said in a statement to CNN: “The whale continues to appear safe and well which is allowing us time to ensure we assess all the options available and the associated risks. These options range from minimal intervention as we continue to monitor the whale, to actively intervening to attempt supporting the animal to move out of the river.
“The highest tide of the year will take place in a few weeks so there is a window of opportunity for it to be able to head out to sea. We are continuing to consult with experts and our experienced Park staff to ensure our plans are achievable and safe for both the whale and those involved in the operation.
“We are also looking at a range of options to map the riverbed to find the deepest channel through which the whale could travel to sea and we are seeking advice from the staff who are most familiar with this river.”
It is home to many animal species, including crocodiles and flatback turtles. It also describes itself as a “living cultural landscape” as its archaeological sites record the skills and way of life of indigenous people over tens of thousands of years.