He asked that Khaleda's experiences in dealing with the Rohingyas be used to come to a collective solution
Addressing the prime minister, he said: "The Rohingya issue is a national crisis, and it cannot be solved by one particular party. It is a question of Bangladesh's existence. I call for a national dialogue."
Rizvi also demanded that BNP Chairperson Khaleda Zia's experiences in dealing with the Rohingya crisis be used to solve the issue.
He made the demands at a press briefing held at BNP's central headquarters in Naya Paltan on Thursday.
Rizvi criticized Prime Minister Sheikh Hasina's comments made in the Parliament on Wednesday, where she said the Rohingya crisis was created by Ziaur Rahman.
The BNP senior joint secretary general said: "The prime minister made such comments to cover her own government's failure to deal with the crisis."
He added: "Nobody can make such a comment without being insane."
Calling for a dialogue between the prime minister and Khaleda Zia, the senior BNP leader said: "If Khaleda Zia is freed, then we can put her experiences into working together to solve the problem."
Talking about Khaleda Zia's health, Rizvi said: "Everyone knows you cannot get proper treatment inside a jail.
"The government, in blind vengeance, is slowly pushing Khaleda to her death by creating obstacles against her receiving proper treatment," he said.
The BNP joint secretary general further claimed that the government is openly intervening in court matters to stop Khaleda from securing her bail.
Earlier on Thursday, BNP Chairperson Khaleda Zia filed an appeal with the Appellate Division against the High Court order that had rejected her bail plea in the Zia Charitable Trust graft case.
A High Court bench rejected her bail petition, in which Khaleda had been sentenced to seven years’ imprisonment, on July 31.
Rizvi also accused the authorities of Bangladesh Sheikh Mujib Medical University (BSMMU) of not taking proper steps to ensure Khaleda's treatment.
However, despite Rizvi claiming that no physician had gone to check on Khaleda in the last week, Khaleda's sister Selima Begum told reporters on Wednesday that Khaleda regularly goes through check-ups.
"But she is not receiving proper treatment," Selima added.