Sheikh Hasina's Awami League is not accepting defeat
International monitors have said Monday's voting was mostly free and fair, despite one of the bloodiest election campaigns in the country's history.
But the outgoing government, led by Sheikh Hasina, is refusing to accept defeat. The Awami League has now said its MPs will boycott parliament until its demand is met, the AFP news agency reports.
Specific complaints
"We want fresh elections across Bangladesh," Awami League Secretary-General Zillur Rahman told AFP.
"We have given specific complaints to the Election Commission," he was quoted as saying.
Unofficial results reported by state media give Khaleda Zia's Bangladesh Nationalist Party just over 200 of a possible 300 parliamentary seats.
A total of 17 constituencies are repolling and one postponed the vote because a candidate died.
Mrs Zia was due to meet the head of the caretaker government on Wednesday to discuss the formation of her new administration.
A BBC correspondent in Dhaka says the key factor behind Mrs Zia's victory was perhaps her ability to exploit resentment throughout the country over the breakdown of law and order.
The country is also plagued by corruption. Cabinet talks
Mrs Zia has also held talks with Islamic fundamentalist members of her four-party coalition to discuss cabinet seats.
Mrs Zia, who was last in power in 1996, is expected to be formally announced as premier by President Shahabuddin Ahmed within the next two days.
Despite the Awami League's rejection of the result, sources within her party have conceded the overwhelming defeat should lead to reflection, not protest.
"We need a proper evaluation of why we faced a disaster in the polls," one anonymous party source told the Reuters news agency.
In a brief post-election address Mrs Zia called upon her supporters not to take revenge for any injustices they may have endured in recent years.
The BBC's Alastair Lawson in Dhaka says this is clearly meant as a message of reconciliation after a campaign in which 140 people were killed.
Further unrest
The poll was preceded by the most violent campaign in the country's 30-year history and diplomats warn that further unrest could follow - they say there is a strong possibility that angry supporters of the losing party will take to the streets.
Our correspondent says it is a devastating defeat for the Awami League.
Most cabinet members have lost their seats and the party has been wiped out in its traditional heartlands, such as the capital.