"It is not possible for us to compromise with those who celebrate a 'fake birthday' on the death anniversary of Bangabandhu Sheikh Mujibur Rahman," ruling Awami League general secretary and Local Government Minister Syed Ashraful Islam said.
"Many things could be said under political consideration, but celebrating your birthday on the day we lost the Father of the Nation is not a political issue," Islam added.
Hasina too slammed her archrival in an emotion choked voice for celebrating a "fake birthday" on Thursday by cutting huge cakes, including one weighing 69 pounds to indicate she had turned 69.
Bangladesh observes National Mourning Day on August 15 to mark the 1975 assassination of Rahman, fondly called 'Bangabandhu' or 'Friend of Bengal', and most of his family in a military putsch. Hasina and her younger sister survived as they were abroad at that time.
Also Read
They said Zia's marriage certificate mentions she was born on September 5, 1945, her first passport states the date of birth as August 19, 1946 while her registration for the matriculation or school final exams states she was born on August 9, 1944.
The birthday controversy began in 1991 when Zia first celebrated it on August 15 after assuming the office of premier and declared the date as her "official birthday".
Despite criticism from the Awami League, Zia's BNP party went ahead with the birthday celebrations.
Without responding to the criticism, another senior BNP leader, Mirza Fakhrul Islam Alamgir, said it was unlikely that the ruling and opposition parties would be able to forge consensus on electoral reforms.
"From the statements of the Prime Minister and other government officials, it seems that there is no chance of mutual understanding between the Awami League and BNP over the elections," said Alamgir.
Analysts believe the latest controversy could further strain relations between the two major parties against the backdrop of growing political uncertainties ahead of next year's general election.