Thirteen people have been killed and thousands injured in clashes between supporters of Hasina's ruling Awami League and activists of the opposition Bangladesh Nationalist Party (BNP).
According to results announced until 11 pm, the ruling Awami League party won 90 seats, followed by its key ally the Jatiya Party at 13, bdnews.24 reported. The channel called the election's in Hasina's favour.
"We reject the results and demand a new election under a neutral government", Kamal Hossain, an octogenarian worldwide jurist who heads the opposition alliance, told a news conference.
It stitched together the National Unity Front alliance with smaller parties, but has alleged its supporters and candidates faced attacks and intimidation, including shootings and arrests, at the hands of ruling party activists during campaigning.
Hasina, 71, has been lauded for boosting economic growth in the poor South Asian nation during her decade in power and for welcoming Rohingya refugees fleeing neighboring Myanmar.
The election campaign has been marred by allegations from the opposition of arrests and jailing of thousands of Hasina opponents. According to the Election Commission, 1,848 candidates are contesting for 299 out of 300 Parliament seats.
"Voters are not allowed to enter booths". Awami League supporters had set up help desks on the street outside the polling station for voters to find their registration serial numbers.
Bangladesh has tightened security ahead of Sunday's elections, deploying some 600,000 police, army and other security forces.
Under the Constitution, the president will call the winning party or alliance to form a government after a formal declaration of results.
"I want to say, maybe the BNP would say at one point of the election that they are withdrawing from the race, we will not compete".
Authorities have ordered the country's mobile operators to shut down 3G and 4G services until midnight on Sunday "to prevent the spread of rumours" that could trigger unrest.More news: Reduction of USA troops diplomatic victory for Pakistan
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The broadcaster, which is owned by Jamuna Group - one of Bangladesh's biggest conglomerates, which also runs a newspaper - is known for its independent coverage.
In the first fully-contested elections in the country for 10 years, there have been local reports of 16 people being killed in election-related violence.
This election, some 104 million people are eligible to vote, including many young, first-time voters.
With 267 seats under its belt this time, the ruling alliance has surpassed its 2008 poll success - when it had secured 263 parliamentary seats. It was the highest level of security, so that the election could take place in a "peaceful atmosphere", said Rafiqul Islam of the election Commission.
Bangladesh is a country of 165 million but turnout was reported to be low with the prime minister predicted to win so easily.
Sunday's deaths brought to 18 the official police toll for election violence since the ballot was announced on November 8. She has already invited foreign journalists and poll observers to her official residence on Monday.
While rights groups have sounded the alarms about the erosion of Bangladesh's democracy, Hasina has promoted a different narrative, highlighting an ambitious economic agenda that has propelled Bangladesh past larger neighbors Pakistan and India by some development measures.
"I believe that people will cast their votes in favor of Awami League to continue the pace of development", Hasina told reporters in Dhaka.
Hasina appeared as the first voter in Dhaka centre from where her nephew and party candidate Fazle Nur Taposh was a contender.
The sample size of the survey was 2,249 and the respondents were drawn from the constituencies of 51 parliamentary seats on December 9-16, said Forrest E. Cookson, an American consultant who presented the findings at a news conference.
Human Rights Watch and other global groups have decried the crackdown, saying it has created a climate of fear which could prevent opposition supporters from casting ballots.
The country's Election Commision told a news agency that it is also investigating claims of vote rigging across the nation.