Hasina's alliance is on strike to demand changes to the electoral commission and voter list. The alliance says the current commission and list favour Zia's party.
Zia's four-party coalition disputes the claim, and wants the elections to go ahead as scheduled on January 21.
Iajuddin Ahmed, the president of Bangladesh and head of the interim government, was set to meet advisers on Monday to discuss how to end the standoff, his office said.
Mahbubul Alam, one of three advisers in a government delegation, said his team had met separately with Zia and Hasina.
Alam said the talks with Zia were positive and that they had "discussed issues related to holding the elections in a free and fair manner".
In the meeting with Hasina, "we openly discussed the government's position on their demands," Alam said.
Ahmed, charged with leading the caretaker government until the January elections, also held separate meetings on electoral reform with the political rivals on Saturday, but made no progress.
Fayez Ahmed, 25, a local leader of the student wing of Zia's Bangladesh Nationalist party, was among the three people killed since Sunday. A further 50 people have been injured, an official said on condition of anonymity.