The deaths came as the Bangladesh National Party (BNP) called a 48-hour strike demanding the elections be suspended, Gulf News reported.
The BNP has called for Prime Minister Shaikh Hasina to resign so a neutral caretaker government can oversee the Jan. 5 election.
Kazi Rakibuddin Ahmad, the nation's top elections official, announced Monday the elections would be held because the commission was constitutionally mandated to hold an election by Jan. 24. He said the commission had waited for the major political parties to come to an agreement over their disputes, "but now we don't have time to delay further."
Dec. 2 is the last date candidates can submit their names for inclusion on ballots.
Opposition parties have been campaigning to create a non-partisan government led by an "acceptable" person to oversee the election.
The government removed 30 ministers last week from the ruling alliance led by the Awami League and reconstituted the cabinet to form an "all-party" government to act in the run-up to the election.
The BNP called the new cabinet a farce because elections under Hasina would not be credible.