Bangladesh awarded the US company rights to explore in blocks 10 and 11 in the energy-rich Bay of Bengal in 2011 after Myanmar found a huge gas reserve in nearby waters.
But after conducting two surveys, ConocoPhillips has told Bangladesh's state energy group PetroBangla it will not continue exploring, the country's junior energy minister Nasrul Hamid told AFP.
"We have come to know they (ConocoPhillips) are going to pull out of the blocks No. 10 and 11," Hamid said.
In an email to the Dhaka Tribune newspaper, ConocoPhillips Bangladesh managing director Thomas J Earley was quoted as saying the firm was unable to justify drilling.
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"We have therefore decided not to continue petroleum operations and the PSC (production-sharing contract) will terminate on December 15, 2014," Earley wrote.
The Bangladesh minister said the company wanted to raise the price agreed in the 2011 contract, arguing the current rate at which it has to sell up to 75 per cent of the gas to Petrobangla was too low.
Bangladesh recently resolved its longstanding maritime boundary disputes with Myanmar and India to try to make way for hydrocarbon exploration in the Bay of Bengal.
It is urgently attempting to locate new sources of energy as the government has said current gas reserves may run out by early next decade at present rates of consumption.