"You could not resist the elections. You'll not be able to do anything. Better keep your mouth shut," Hasina said.
The general election in Bangladesh were boycotted by the 18-party opposition alliance led by the Bangladesh Nationalist Party (BNP).
Hasina-led Awami League easily won Sunday's election, which was marred by street fighting and low turnout.
Over 30 people have died in post-poll clashes with opposition cadres setting over 200 polling stations on fire.
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The Election Commission earlier said the voter turnout was 40 per cent.
The Awami League chief once again urged Zia to sever ties with the fundamentalist Jamaat-e-Islami and asked her to strike a deal on the next elections.
The BNP, led by former prime minister Zia, boycotted the polls after her arch-rival Hasina rejected the opposition's demand for a neutral caretaker regime for election oversight.
Political violence during strikes enforced by the opposition since November have left over 160 people dead.