Over 12,000 candidates from some 20 parties, including former prime minister Khaleda Zia's BNP, were contesting the polls in which 7 million eligible voters are likely to exercise their franchise to elect mayors and councillors in 234 municipalities.
The polls saw Bangladesh Nationalist Party (BNP) and ruling Awami League facing each other off, though a large number of political groups and independent candidates were also contesting.
Bangladesh is unlikely to see any change in the government until the 2019 general elections, but analysts said today's polls appeared to be a referendum on the popularity of Prime Minister Sheikh Hasina's Awami League and Khaleda's BNP.
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.
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But reports said clashes occurred in northeastern Satkania, where a man was killed when supporters of two candidates traded gunshots.
Reports said authorities postponed polling at nine centres of six municipalities as violence erupted over alleged rigging by mayoral candidates.
Awami League leaders said barring few incidents, polling was peaceful while BNP alleged that the ruling party workers occupied several polling centres soon after the voting began.
The municipal polls came as Bangladesh in October amended a century-old system of electing local government bodies on non-partisan basis with the parliament approving a proposal to allow political parties to contest local government polls.