Voting began at 8 am (local time) in the morning with Prime Minister Sheikh Hasina appearing as the first voter in Dhaka centre from where her nephew and party candidate Fazle Nur Taposh was a contender.
"I'm always confident about our victory in the elections... I trust my people and I know that they will choose us so that they can get a better life in future," Hasina said after casting her vote.
While Hasina is seeking re-election for a fourth term as the prime minister, her rival ex-premier and BNP chief Khalida Zia, who is reportedly partially paralysed, faces an uncertain future in a Dhaka jail.
Schools and colleges across Bangladesh were turned into makeshift polling centres for the day while people had begun to line up to cast their vote even before the election opened.
Meanwhile, violence marred the polling in parts of the country with media reports putting the death toll at 11. Dozens of people were wounded in the poll-related violence.
A Jubo League - the youth wing of the Awami League - leader was killed and 10 others injured in a clash between the ruling party and opposition BNP supporters in Rangamati's Kawkhali, Bdnews24 reported.
One BNP activist was killed in Chattogram, while an Awami League supporter died in Rajshahi, the news portal reported.
An Awami League polling agent was killed in Narsingdi 3 constituency.
According to the Daily Star newspaper, BNP men attacked and killed an Awami League supporter in Mohonpur, Rajshahi-3. One Oikyafront supporter was killed in Chandina in police firing.
A voter died during tension between supporters of the Awami League and the BNP in Dinajpur-2. An activist of Bangladesh Chhatra League was killed in clashes with the BNP activists in Cox's Bazar-1.
One Awami League supporter was killed during a clash with the BNP workers at Baghail Government Primary Schoo, under Bogura-4.
A member of law enforcement agency was killed by activists of Jamaat in Noakhali-3 constituency.
At least seven candidates - six being BNP nominees - announced to stay off the polls with most of them alleging that their agents were ousted from polling centres by the ruling party workers.
BNP's Ruhul Kabir Rizvi alleged that polling centres are being occupied across the country, the party's agents are being driven out and that its supporters and activists are facing violence.
"From the picture we have received, this is a violent election. We are seeing a one-sided election environment conducted at the whims of the government. This paints a clear picture that they want to ensure a favourable result through a one-sided contest," Rizvi told a media briefing at the party office.
Party's secretary general Mirza Fakhrul Islam Alamgir told the media from his northwestern Thakurgaon constituency that some of their candidates stayed off the vote in their "personal decisions" but "we will announce our party stance at 4 PM when the voting will end".
Jatiya Oikya Front (National Unity Front) leader Kamal Hossain expressed concern over the poll-related violence and allegations of rigging.
"Every minute I receive calls saying Kamal Bhai (brother), it has already happened overnight. It began in the evening. I have gotten so many reports. These reports are concerning. It's sad and shameful," he said.
The Jatiya Oikya Front is a coalition of four parties - Gono Forum, BNP, Jatiya Samajtantrik Dal-JSD, Nagorik Oikya and Krishak Sramik Janata League - led by Hossain.
Bangladesh police chief Mohammad Javed Patwary said the nationwide polls are "progressing peacefully" and vowed to investigate the "isolated" incidents of violence.
Over 600,000 security personnel including several thousand soldiers and paramilitary border guards have been deployed across the country to help conduct the election in which 10.41 crore people are eligible to vote.
Security agencies have been asked to keep an extra vigil on religious minority communities as media reports said at least three Hindu households were set on fire by miscreants between December 16 and 26.
According to the eyewitnesses, posters bearing the ruling party's "boat" symbol outnumbered those of the main opposition's "sheaf of paddy".
BNP earlier said intimidation and police harassment kept their activists away from the campaign and polling process.
"Barring some unwanted incidents, the polling so far was smooth and peaceful...We could tell you at the end of the day if the election was participatory," Chief Election Commissioner Nurul Huda told reporters.
The 11th parliamentary poll is the first fully competitive general election in a decade since 2008 while it is widely expected to be won by the Awami League of Hasina, who is likely to be the country's first premier for the fourth terms.
Citing security reasons, authorities temporarily blocked mobile data services and slowed down the internet.
According to the Election Commission, 1,848 candidates are contesting for 299 out of 300 Parliament seats. The polls are being held at 40,183 polling stations. Voting was suspended in one seat due to the death of a candidate.
Zia, serving a 10-year prison term on graft charges, has been barred from contesting the polls while Rahman is living in London.\
(With PTI inputs)