Ahmed's attempt to end violence in the country included the postponement of elections scheduled for January 22.
"Political animosity, mistrust and violence have made life miserable for the people and made the future of democracy uncertain," Ahmed 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.
The elections are being boycotted by a multi-party alliance headed by Sheikh Hasina, the former prime minister.
|"Political animosity, mistrust and violence have made life miserable for the people and made the future of democracy uncertain"|
At least 45 people have been killed and hundreds injured in violence since Begum Khaleda Zia 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 Ahmed'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," added the official, who requested anonymity.
Troops that were deployed before Ahmed declared a state of emergency continued to patrol the streets of Dhaka and elsewhere in the country in the early hours of Friday.
Ban Ki-moon, the UN secretary-general, noted 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," Ban 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," Ban said.
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 Hasina's 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 try to disrupt it with daily strikes and blockades.