The IndiGo flight in which Mamata was traveling in from Patna to Kolkata reportedly went short of fuel and hovered around the airport for nearly 30 minutes as it waited for clearance to land.
On touching down, fire engines and ambulances surrounded it as a standard protocol for emergencies.
"The plane was about to crash... we want to bring to notice that life of Mamata Banerjee is in danger," Sudip Bandyopadhyay from TMC said in Parliament.
According to sources, as the flight was an hour late to take off from Patna, it was in line of planes waiting to land. Thus, congestion was the main reason behind the delay, said sources.
However, her party says the plane should have been prioritised as the Chief Minister was on the flight.
Meanwhile, IndiGo said in a statement that the flight made a normal landing and it was kept on hold due to air traffic congestion. It also clarified that IndiGo Captain at no stage declared a fuel priority or an emergency.
Over the past few weeks, Mamata has been protesting against Prime Minister Narendra Modi's demonetisation move.
The TMC appears to link her delayed plane landing incident with her clashes with the government.
"Is there more to this than meets the eye?" asked Derek O'Brien, also of the Trinamool. There is a school of thought that this is a conspiracy," he said in the Rajya Sabha.
An inquiry has been ordered to find out why the plane did not have required fuel, Civil Aviation Minister Ashok Gajapathi Raju said.
"There was no conspiracy against the Chief Minister," the eastern chief of the Airports Authority of India, Sanjay Jain, said.
Full statement of IndiGo:
"This is to inform that IndiGo flight 6E 342 from Patna and Kolkata made a normal landing at the Kolkata airport on Wednesday, November 30.
The flight was kept on hold for landing due to air traffic congestion at Kolkata. The pilot operating 6E-342 had advised the ATC that he has 8 mins of extra holding fuel over Kolkata (Destination) before commencing diversion to the planned alternate."
"However, this information was misunderstood by the Air Traffic Controller who assumed that the aircraft had only 8 mins of total fuel left.
The misinterpretation of the information by ATC controller led ATC to instruct fire engines and ambulances to be stationed at Kolkata airport. We would like to clarify – IndiGo Captain at no stage declared a fuel priority or an emergency."
"Subsequently, the airplane made a normal landing at Kolkata airport at 8 40 PM (Delayed by an hour due to congestion). The fuel on arrival was more than the minimum diversion fuel. There has been no violation or breach of any regulatory requirement in the above-mentioned scenario."
"IndiGo has responded to the queries made by the regulator. At IndiGo, safety of passengers, crew and the aircraft is the utmost priority and at no stage it can be compromised."