The demand has piled pressure on President Maithripala Sirisena, who won elections in January last year on a promise to end cronyism and corruption, from his own Freedom Party.
"If (Mahendran's) conduct had been found undesirable he should be removed for the good of the President and the Prime Minister," Minister of Petroleum Chandima Weerakkody said.
Mahendran, who was appointed as Central Bank Governor by Prime Minister Ranil Wickremesinghe, has been under fire since March last year after his son-in-law was accused of unduly benefiting from a USD 76 million bond auction.
They allege that the family member benefited from inside information about the rate and volume of bonds the bank planned to issue.
The Central Bank governor, whose term is set to end at the end of this month, has denied any wrongdoing.
