Hasina's ruling alliance won more than 90 percent of the seats contested in Sunday's election, which was marred by accusations of ballot stuffing, voter intimidation and violence that killed at least 19 people.
Opponents rejected the election result but Hasina and her Awami League have denied any impropriety, saying that the vote was peaceful and there was enthusiastic participation from her supporters.
"We urge the authorities to carry out prompt, independent, impartial and effective investigations into all alleged acts of violence and human rights violations related to the elections, with a view to holding accountable those responsible, regardless of their political affiliations," the United Nations said.
On Thursday, newly elected members of parliament, including Hasina, were sworn in, but the seven opposition members stayed away, saying the results were rigged and calling for a new election.
"There are worrying indications that reprisals have continued to take place, notably against the political opposition, including physical attacks and ill-treatment, arbitrary arrests, harassment, disappearances and filing of criminal cases," the United Nations said.
"Reports suggest that violent attacks and intimidation, including against minorities, have been disproportionately carried out by ruling party activists, at times with complicity or involvement of law enforcement officers."
The United Nations called on the authorities to take urgent measures to prevent further reprisals, and to ensure that law enforcement authorities exercised their powers in accordance with the rule of law.
It also urged the national Human Rights Commission to play an independent and proactive role.
Western governments, including the United States and the European Union, have condemned the election-day violence and called for an investigation into a range of irregularities.
On Thursday, New York-based Human Rights Watch said the run-up to the vote was characterised by "violence and intimidation against the opposition ... and the misuse of laws to limit free speech".