Hasina dubbed the BNP chief a "murderer" and "leader of the militants" and asked her to surrender before a Dhaka court which last month issued a warrant ordering her arrest in two graft cases.
"What is there to talk about with her?" she said.
"Khaleda (Zia) did not get the support from the West (western countries) as well as the North (a reference to the army) and that is why she is burning people from her rage," Hasina said.
"The movement will continue until a logical consequence. I urge all to accept the trouble in the greater national interest," the ex-premier said in her second such public appearance since the beginning of the unrest coinciding with the first anniversary of last year's elections which BNP boycotted alleging it lacked "level playing field".
"Otherwise, the government will be compelled to execute the court's order," the premier said.
But Hasina-led Awami League, meanwhile, said the dialogue could be held only if "she (Zia) stopped killing people, holding back her terrorist forces" as it called a press conference in response to Zia media briefing.
"No country in the world held talks with terrorists, Bangladesh will be no exception. They (BNP) have launched a war against the people and so we will also fight back but if they stop arson attacks, killing of people to create a peaceful atmosphere, the dialogue may be held," the ruling party's general secretary and minister Ashrful Islam said.
Meanwhile, BNP overnight called a fresh 72 hours nationwide strike from tomorrow issuing a statement hours after Zia's media briefing, protesting against the "arrest" of one of the party's leaders Salahuddin Ahmed three days ago by plainclothesmen.