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With the opposition already having called a 48-hour strike and seven people killed in clashes on Monday, the crisis showed no sign of easing, risking further unrest and damage to the $22 billion garment industry, which accounts for 80 percent of the country's exports.
Hasina's Awami League ended with more than two-thirds of seats in a contest that was shunned by international observers as flawed and derided as a farce by the opposition Bangladesh Nationalist Party (BNP). With fewer than half the seats contested, the outcome was never in doubt.
"An election can happen any time when BNP comes for a dialogue, but they must stop violence," Hasina, 64, said on the lawn of her official residence.
Many BNP leaders are in jail or in hiding, and party chief Begum Khaleda Zia says she is under virtual house arrest, which the government denies.
"The ongoing crisis will not be resolved by keeping me virtually confined to my house and carrying out oppression on the opposition," Khaleda said in a statement on Monday, urging a new election.
Hasina and Khaleda, 68, are bitter rivals who have alternated as prime minister for all but two of the past 22 years.
The United States said it was "disappointed" by the election. "The results ... do not appear to credibly express the will of the Bangladeshi people," a statement from the US State Department said.
It called on the government and opposition to engage in immediate dialogue to find a way to hold "free, fair, peaceful, and credible" elections as soon as possible.
It condemned the violence and said citizens must be free to express their views.
"Bangladesh's political leadership - and those who aspire to lead - must do everything in their power to ensure law and order and refrain from supporting and fomenting violence, especially against minority communities, inflammatory rhetoric, and intimidation," the statement said.
Ataur Rahman, a professor of political science at Dhaka University, said the standoff imperils the momentum of five years of robust growth in the impoverished nation of 160 million.
The economy grew 6 percent in the fiscal year that ended in June, and multilateral agencies expect growth of 5.5 to 5.8 percent in the current year.
"The longer the impasse, the longer Bangladesh suffers," Rahman said. "And unfortunately everyone understands this other than our two top leaders."
The BNP denounces Hasina's scrapping of the practice of having a caretaker government oversee elections. The Awami League says the interim government system has proved a failure.
With the BNP on the sidelines and voters worried about violence, turnout was expected to have been low.
An election official, who declined to be identified because the figure was not final, told Reuters that turnout was nearly 40 percent. A monitoring organisation, the Election Working Group, had put turnout at 30 percent, according to the Dhaka Tribune.
In the last election, in 2008, a record 83 percent of voters cast ballots. In a 1996 election boycotted by the Awami League, 21 percent voted.
The European Union, a duty free market for nearly 60 percent of Bangladesh's garment exports, refused to send election observers, as did the United States and the Commonwealth, a grouping of 53 mainly former British colonies.
"It is ... disappointing that voters in more than half the constituencies did not have the opportunity to express their will at the ballot box and that turnout in most other constituencies was low," Sayeeda Warsi, a senior British Foreign Office minister, said in a statement.
Five people were killed on the outskirts of Dhaka on Monday in a clash between supporters of rival parties, with two more fatalities in rural areas, continuing a spate of violence in which 18 people were killed during polling on Sunday and more than 100 in the run-up to the election.