Bangladesh has been under a state of emergency since the interim government, headed by former central bank governor Fakhruddin Ahmed, took power following widespread political violence.
The success or failure of Monday's polls will be seen as an important indicator for general elections, which were cancelled by the interim government in 2007, due to be held next year.
Nazmul Ahsan Kalimullah, chairman of the National Election Observation Council, a local monitoring group, said: "So far we have noticed no anomaly or breach of the codes of conduct".
The elections are the first in the country's history to use a digital voter list with photographs to confirm a voter's identity and avoid multiple voting, problems which have plagued previous ballots.
"This is the first opportunity we have in many years to elect a mayor and councillors in a free and unintimidating atmosphere," one voter said.
Sajjadur Rahman, a deputy police commissioner in northern Rajshahi city, said voting had been "disciplined and peaceful".
ATM Shamsul Huda, the chief election commissioner, said the local polls a "gateway to democracy".
Candidates running in Monday's elections were registered as independents because Bangladesh's election laws curprevent political parties from directly contesting local councils.
Candidates running in Monday's elections were registered as independents because Bangladesh's election laws curprevent political parties from directly contesting local councils.
However, after a ruling last week by the high court, political parties will be able to field candidates during additional rounds of local polls in coming weeks.
Officials say the ruling will help candidates prepare for a national election expected in December.