Hasina asked main opposition Bangladesh Nationalist Party leader and her arch-rival Khaleda Zia to stop "killing people in the name of political movements and come to an agreement."
"We can hold fresh elections dissolving (the 10th) Parliament if we reach a settlement through negotiations," the Awami League president said.
Hasina also added that "there was no scope for them (opposition) to take part in the January 5 polls", since they have failed to nominate candidates.
"Parliament will be convened after the election and talks will be held to evolve a consensus for holding the 11th parliament polls," Nasim told a press conference at the party office.
Also Read
UN chief Ban Ki-moon's envoy Oscar Fernandez-Taranco came to Dhaka in early December and made Awami League and BNP leaders to hold dialogue to find a political solution.
"Talks are ongoing and it will continue even after the general elections," said the Prime Minister.
Former premier Zia-led BNP, Jamaat and their smaller allies have been staging protests since late October to try to force Hasina to step down so that a neutral caretaker government can oversee the election.
Hasina is refusing to accept the arrangement, which was in place during previous national polls.
The BNP has refused to field candidates for the January election, saying the vote under Hasina will be rigged - an accusation the premier flatly rejects.