The poll by the Dhaka Tribune newspaper found that 77 per cent of people felt the polls without the Bangladesh Nationalist Party (BNP) would not be acceptable, while 71 per cent believed the country is going in wrong direction.
However, around 41 per cent of respondents said they would cast their votes even if it is not an inclusive election.
An 18-party opposition alliance led by the BNP decided to boycott the polls after its demands for Prime Minister Sheikh Hasina's resignation and installation of a non-party caretaker government to oversee the elections were turned down.
The nationwide opinion poll, based on interviews of 2,438 respondents, said had the BNP participated, the polls could have been a neck-and-neck fight between the two major parties - the Awami League having 36 per cent support and the BNP enjoying 37 per cent.
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The poll interestingly indicated that more male voters intend to vote for the BNP than the Awami League, while more women would vote for the Awami League.
The survey was conducted between December 14 and 22 last year over mobile phones - a method which Gallup, a US-based performance-management consulting company, follows in such opinion polls.
Around 47 per cent of respondents said the current government is sufficient for holding free and fair elections, with 23.21 per cent saying the country is on the right track.
As many as 74 per cent respondents are either satisfied or highly satisfied with the trial of the war criminals. Over 53 per cent people have opposed the ban on the fundamentalist Jamaat-e-Islami party's participation in the polls while 33.3 per cent support the prohibition.
"This points to a swing [of the voters] to the BNP from the last elections, fully in line with the history of anti-incumbent swings in the national elections," the survey said.