Later, though, he lifted the curfew as well as all curbs on the media.
Stores opened and cars filled the streets of Dhaka, and by late morning on Friday, life appeared largely normal across the country.
Fakhruddin has the task of steering the country through one of the most serious political crises in its history.
The country's two main political leaders made no comment about his appointment, but one of them - the Awami League's Sheikh Hasina Wajed, a former prime minister - attended the swearing-in.
Iajuddin's attempt to end violence in the country included the postponement of elections.
"Political animosity, mistrust and violence have made life miserable for the people and made the future of democracy uncertain," he said in a televised address late on Thursday.
A presidential spokesman said it was impossible to hold the elections as planned because most of the president's council of advisers had quit.
Asked when they might be held, the spokesman said: "It will be decided in due course."
Government officials said privately that it could take months before a new ballot took place.
Earlier on Thursday, the UN announced it would suspend all technical support for the elections while the European Commission suspended its observation mission to the polls due on January 22.
|Fakhruddin Ahmed has taken charge at a|
critical moment in Bangladesh's history
The elections are being boycotted by an Awami League-led multi-party alliance.
At least 45 people have been killed and hundreds injured in violence since Begum Khaleda Zia of the Bangladesh Nationalist Party stepped down as prime minister in October at the end of her five-year term, handing power to the interim authority which was charged with organising polls.
There are now hopes that Iajuddin's resignation will stem the violence.
"His stepping down as caretaker chief has relieved the nation from months of tension," one senior official said.
"But it remains to be seen how the country now proceeds towards an election with all parties participating and acceptable to all."
Ban Ki-moon, the UN secretary-general, said the situation in Bangladesh had deteriorated to the point that the US-based National Democratic Institute for International Affairs and the International Republican Institute were refusing to monitor the elections.
"The political crisis in Bangladesh has severely jeopardised the legitimacy of the electoral process," he said in a statement released on Thursday in Dhaka.
"The United Nations has had to suspend all technical support to the electoral process, including by closing its International Coordination Office for Election Observers in Dhaka."
Technical support includes consulting and advice on publishing results as well as ballot casting and counting.
Ban urged the army to stay neutral.
Hasina and her successor Khaleda have been foes since 1991 when they jointly led a people's revolt that ousted military ruler Hossain Mohammad Ershad.
But the Awami League and its allies have continued to accuse the interim government of bias in Khaleda's favour and, on Wednesday, said they would not only boycott the election but also try to disrupt it with daily strikes and blockades.