Hasina, 66, was accompanied at Sheik Mujibur Rahman's shrine by her ministers and advisers who make up the government's 49-member Cabinet, the Bangladesh Daily Star reported.
Hasina, who was re-elected this month, condemned the opposition Bangladesh Nationalist Party and its partners for boycotting the election and not running candidates.
She said their boycott was a lost opportunity to build democracy in Bangladesh.
Hasina and her Awami League party Cabinet were sworn in during the weekend after a bitterly fought national election that was marred by violence, deaths and the destruction of polling stations.
The BNP, leading an 18-party alliance, had demanded that a caretaker government oversee the Jan. 5 election.
Hasina's election continues an Awami League and familial dynasty for Bangladesh, which as East Pakistan fought a war for independence from West Pakistan in 1971.
Hasina has led the Awami League since 1981. She was elected prime minister for the first time in 1996 and served until being defeated by the Four Party Alliance, led by the BNP, in the 2001 general election.
Hasina, who was elected again in 2009, is the eldest of five children of Rahman, the first president of Bangladesh. Rahman was assassinated in 1975.
During her swearing-in ceremony, Hasina hit out at the BNP, saying there won't be political reform discussions with the party until civil disruptions stop, Bangladeshi Internet news site bdnews24.com reported.
"The obstacle they have created in people's lives and livelihoods has to stop," she said.
She said the BNP, by not contesting many constituencies, has detracted from Bangladesh's democracy and that BNP leader Khaleda Zia knows the party's actions were wrong.
Zia, who has led the BNP since 1981, was prime minister from 1991-96 and 2001-06.
"I do not know who advises them [the BNP], but now she realizes her mistake," Hasina said.
"It's regrettable that they have not done their duty to strengthen the base of democracy. If they had participated, the base of democracy would have been stronger."
The international community has called for a rerun of the election amid fears of more unrest.
The BNP led a nationwide 48-hour strike after Zia said the election was a "scandalous farce" and urged her supporters to boycott the polls.
Violence ensued and at least 18 people were killed and more than 100 polling stations burned on election day, the BBC reported.
The BNP and other protest groups have vowed to continue their demonstrations that include blockading roads, railways and waterways.
Notable deaths of 2014 [PHOTOS]