The UN High Commissioner for Human Rights also voiced concern about the detention of key opposition leaders in the unrest, which has killed 50 people since late October when the government first announced the date of the general elections.
"Whatever their differences, political leaders on both sides must halt their destructive brinkmanship, which is pushing Bangladesh dangerously close to a major crisis," Pillay said in a statement.
In the latest incidents, one demonstrator in Bangladesh was shot dead by officers yesterday and another died late Friday as police used live ammunition, rubber bullets and tear gas to disperse protesters.
Opposition groups led by the Bangladesh Nationalist Party (BNP) as well as its Islamist allies are demanding that Prime Minister Sheikh Hasina resign and make way for elections under a neutral caretaker government.
Hasina has rejected their demand and is sticking to her January poll plans.
"In the past week, we have seen acts as extreme as protesters throwing molotov cocktails onto public buses without allowing the occupants to escape, leaving women and children with horrific burns," she said.
"Such levels of violence are deeply shocking for the Bangladeshi people, the vast majority of whom want - and deserve - a peaceful and inclusive election.
