The incumbent interim government, headed by former central bank governor Fakhruddin Ahmed, is keen for both parties to take part in the next elections, which analysts and diplomats say will not be credible without them.
The BNP said it was waiting for Khaleda's release and her sons to be sent abroad for treatment, a move that would create conditions for the party to hold discussions with the government about the upcoming December polls.
But party secretary-general Khandaker Delwar Hossain said neither Khaleda nor her party would make an appeal - like Hasina did - to the interim government for her freedom.
"We demand they (Khaleda and sons) be freed immediately and it is the government's obligation to set them free, to prove its goodwill to hold a credible election and restore democracy," Delwar said.
Hasina was granted an eight-week parole on Wednesday for medical treatment abroad after spending 11 months in jail for alleged corruption. Her party subsequently said they would participate in talks with the interim government on the elections.
Khaleda and her two sons, Tareque Rahman and Arafat Rahman have also been in jail since they were arrested last year for graft and amassing wealth illegally.
Tareque's wife and daughter sent a written appeal to the Interior (Home) Ministry on Sunday seeking his release and foreign medical treatment for back ailments.
Hasina left for the United States on Thursday
Courts prosecuting Hasina ruled before she was paroled that hearings would continue in her absence. The same may happen to Khaleda, who is also being prosecuted for corruption.
Bangladesh's interim government took over in January 2007 following widespread political violence, imposed emergency rules, detained hundreds of key politicians and promised to hold a free and fair election before end of this year.
