She also directed her party activists to thwart any attempt to foil the polls.
Hasina, the Awami League party chief said, the opposition leader would have to face trial for violence during the BNP-led 18-party alliance's agitation programmes, bdnews24.com reported. The opposition is boycotting the polls.
"Election will be held on Jan 5," she said firmly. "I'd like to request everyone to go to the polling centres to vote. Don't think we've won and so there is no need for voting."
A total of 153 candidates have won uncontested in the next parliamentary polls as the opposition decided to stay off. Elections in the remaining 147 constituencies will take place.
Addressing a rally at Dhaka's Uttara, Hasina asked the people to identify those behind the violence during the opposition-enforced programmes.
Hasina addressed three rallies in the capital's Mirpur, Pallabi and Uttara on the first day of the new year.
The prime minister criticised the opposition's ongoing agitation to thwart the polls and warned Khaleda Zia would be tried for the deaths and violence.
"Those who are killing people, unleashing violence in the name of demonstrations, will be tried on this soil. She (Khaleda) will be held responsible for orchestrating (the violence)," Hasina said.