"Today is a black day for Bangladesh," Bangladesh Nationalist Party's acting secretary general Mirza Fakhrul Islam said in a statement.
The BNP along with its allies had boycotted the January 5 polls which were marred by violence and saw a low turnout.
"A scandalous journey of autocratic dictatorship has started by suppressing the democratic spirit," Islam said and asked the ruling Awami League to quit immediately and hand over power to a non-party caretaker administration for holding a free, fair election with the participation of all parties.
This is Hasina's third term as prime minister. She also served as premier during 1996-2001.
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Hasina and her 48-member council of ministers took oath of office yesterday. Besides the 66-year-old Awami League chief, 29 lawmakers took oath as Cabinet ministers while 17 MPs were appointed as ministers of state and two as deputy ministers.
Leaders of the BNP did not attend the swearing-in ceremony.
The Awami League won over two-thirds of 300 seats in parliament in the polls, which were described as a farce by the BNP-led 18-party opposition alliance.