The chief of the main opposition Bangladesh Nationalist Party (BNP) asked the ruling Awami League to stop "harassing" her party leaders and workers.
The 68-year-old former premier also appealed to the government to withdraw cases against her party members to create a conducive atmosphere for the talks.
"We (BNP) were never opposed to talks and still now dialogue is the only way to end the deadlock," Zia told a press conference here.
The opposition tried to derail the polls by calling strikes and blockades. Over 160 people were killed in poll-related violence since November.
The Awami League won over two-thirds of 300 seats in parliament in the polls, which were described as a "farce" by the opposition.
Zia, however, evaded a direct answer to a question on Hasina's demand that she should sever her party's ties with fundamentalist ally Jamaat-e-Islami for resumption of talks.
Zia said Jamaat is a "political party".
The Awami League had joined hands with Jamaat in the past, demanding the installation of a non-party caretaker government while "we (BNP) were in power", she said.
"Not even 5 per cent votes were cast though the subservient election commission has shown the turnout to be as high as 40 per cent...You can't stay long in power using your physical strength," Zia said.
She said the opposition alliance would continue its street protest for a poll-time caretaker regime to hold fresh election.
Besides, Zia announced the opposition would stage mass rallies across Bangladesh on January 20 with the main one being at Dhaka's Suhrawardy Udyan. A nationwide black flag protest will also be organised on January 29.
The new government, however, ruled out speculation that it could be short-lived to pave ways for fresh polls.
"Sheikh Hasina does not give in to any pressure whether it is internal or external. The country is ours...And in the interest of people we will do everything required," the prime minister had said in her first comments after the swearing in on Sunday.
She, however, said the government could hold talks with the BNP only if it cuts ties with "anti-Bangladesh" Jamaat.
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