The extremely rare sighting triggered wonder and excitement when the whale was first seen on Tuesday, but after it was spotted again on Wednesday in exactly the same location, concerns grew that the beluga had got lost and was potentially in danger.
"We are working with other agencies to monitor the situation and ready to provide appropriate assistance if requested", it said.
According to National Geographic magazine, beluga whales can range from 13 to 20 feet in length.
The rare marine mammal, nicknamed Benny, was seen near Gravesend yesterday and appeared to be swimming strongly and feeding in the estuary.
"As I live in Gravesend I had no choice today but to literally run to the River Thames to watch the Beluga Whale".
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India's Ministry of Civil Aviation said in a tweet it had sought an "immediate report" from official agencies. Subsequently, Oxygen masks were deployed for the passengers on board.
The video has since been viewed more than 160,000 times, sparking "River Thames" to trend on Twitter. "There have only been around 20 sightings of beluga whales off the United Kingdom coast previously, but these have occurred off Northumberland, Northern Ireland and Scotland".
The Whale and Dolphin Conservation Society said it was "obviously very lost and quite possibly in trouble".
He urged people to give the whale "space and minimise disturbance".
A female northern bottlenose whale was discovered swimming in the river in central London, going past the Houses of Parliament. They have a rounded forehead and no dorsal fin.
Belugas are commonly found in coastal waters of the Arctic Ocean, but are also at home in large rivers. They can move between salt and fresh water.