Over 12,000 candidates from some 20 parties, including former prime minister Khaleda Zia's BNP, were contesting the polls in which there are as many as 7 million eligible voters for the election of mayors and councillors in 234 cities and towns.
Reports and witnesses said clashes between supporters of two councilor candidates in southeastern Satkania claimed one life while some 75 people were wounded as violence erupted in areas across Bangladesh.
The polls saw Bangladesh Nationalist Party (BNP) and ruling Awami League in a major face-off, though a large number of political groups and independent candidates were also contesting.
At least 25 mayoral candidates from ruling Awami League, BNP announced their withdrawal from the race raising allegations of rigging by rival contenders during the voting.
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BNP demanded re-election in 100 centres for "irregularities".
"We have lodged our complaints (but) the election commission seems to be helpless... However, they (EC) have assured us of looking into the matter according to our allegations," Zia's advisor Khandaker Mahbub Hossain told reporters at the commission office.
"BNP is exposed to a state of wilderness since it was miserably defeated in the 2008 elections while its decision to boycott the subsequent 2014 parliamentary polls visibly affected its organisational morale...It was crucial for the party to take part in the local government polls to secure the party structure," said political analyst Khurshida Huq.
The Election Commission (EC) overnight called out paramilitary Border Guard Bangladesh (BGB), elite anti-crime Rapid Action Battalion (RAB) and coastguards to aide the police force in conducting the polls.
The municipal polls came as Bangladesh in October amended a century-old system of electing local government institutions on non-partisan basis with the parliament approving the proposal to allow political parties in the local government polls like the national elections.