Bangladesh's media have urged Sheikh Hasina to shoulder the responsibility of her landslide election victory and make democracy work.
Ms Hasina's Awami League alliance has won more than 260 of the 300 seats in a poll mostly praised by media, monitors and the international community.
However, the losing BNP alliance has complained of widespread fraud and has not yet said it accepts defeat.
An army-backed government ruled for two years before Monday's election.
The interim government had dismissed the previous administration and cancelled elections due in January 2007 after months of street protests and battles between gangs of rival party supporters spiralled out of control.
The Election Commission has not yet declared a final official result but the Awami League alliance has more than 260 seats and the alliance of the Bangladesh Nationalist Party has just 31. The BNP's Islamist ally, Jamaat-e-Islami, was almost wiped out.
'Lesson from history'
Bangladesh's media welcomed the generally peaceful nature of the election. Their main concern was that the result was accepted and that democracy was made to work.
The pro-BNP Jai Jai Din said it was clear that "people want change through democratic means, not by any other way".
The Daily Star said the "final test of commitment and loyalty to democracy will lie in the losing side gracefully bowing out to the popular verdict".
The New Age said that in the past landslide wins had led to governments behaving undemocratically and suppressing dissent.
"We only hope that the Awami League will take lessons from history."
Ms Hasina had been planning to hold a press conference on her victory on Tuesday afternoon but there was a massive crush of journalists and supporters and the event was postponed until Wednesday.
Reporters were planning questions on how Ms Hasina planned to tackle rising prices, Islamist militancy and the issue of corruption that has dogged both her and her main defeated rival Khaleda Zia.
The BBC's Jill McGivering says Ms Hasina has pledged to curb inflation and improve the economy, but the country's manufacturing industries depend heavily on exports and they may struggle in the global downturn.
Our correspondent says to stay popular, Ms Hasina needs to show quickly that she can introduce policies to ease the burden of widespread poverty and reduce inefficiency in public life.
But another key question will be Khaleda Zia and whether she will accept defeat and co-operate with the government or fall back into former tactics of protest and disruption.
Much of the national media has urged Ms Zia's BNP to accept the results.
But the party has complained of fraud and forgery at more than 200 polling stations and observers say the next two days will be vital as to whether the result is accepted or sparks violence.
"We have reports that BNP supporters were barred from coming to the polls and also were driven away from polling stations in many places," a BNP leader, Rizvi Ahmed, said.
The election saw a massive turnout, overseen by hundreds of international monitors who largely pronounced the election fair and credible.
The US state department said: "All Bangladeshis can take great pride in the success of these elections.
"The high voter turnout underscores the people's desire to see democracy restored."
Indian PM Manmohan Singh congratulated Sheikh Hasina in a telephone call, saying Delhi looked forward to working with her government.
Her administration will take charge in about 10 days.