Announcement of the deadline was made Sunday at a news conference in the Chittagong Press Club, bdnews24.com reported..
Nurul Islam, father of hostage Aminul Islam, said he had been contacted Thursday by one of the pirates, who demanded a $700,000 ransom be paid or the hostages would be killed.
Islam and the parents of another hostage held the news conference to pressure Prime Minister Sheik Hasina to raise the ransom money.
Islam said an Indian hostage had already been killed because his ransom had not been paid.
The Bangladeshi men were among 26 mariners aboard a Malaysian ship, the MV Albedo, when it was hijacked Nov. 25, 2010, on the Indian Ocean.
The pirates took the ship and its crew to a coastal area of Somalia.
Seven sailors from Pakistan were released Aug. 1 after the Pakistani government paid a ransom.