Ahmed spoke hours after the head of the election commission resigned, considered the first step to prepare the troubled South Asian nation for polls that were put off under pressure from an alliance of opposition parties.
Ahmed said: "The nation faces the tough challenge of holding credible elections after undertaking the necessary reforms but we have accepted the challenge.
"We are bound by our pledge to hand over power to an elected government within the shortest possible time after holding free, fair and impartial polls acceptable to all."
Bangladesh was plunged into its worst political crisis in years this month after Iajuddin Ahmed, the president, put off elections set for January 22, declared a national emergency and gave up the post of caretaker chief after weeks of protests.
An alliance of parties led by the powerful Awami League had accused Iajuddin of favouring the rival Bangladesh Nationalist Party (BNP) and boycotted the polls.
Forty-five people were killed and hundreds injured in the protests.
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Iajuddin was replaced by Fakhruddin Ahmed, a respected former central bank governor, who formed a team of 10 advisers last week before preparing for a ballot which some experts say could take at least three months.
Ahmed said the government needed to reorganise the election commission, redo the voters' rolls and arrange for transparent ballot boxes to ensure credible elections which all political parties would contest.
"We want elections and politics to be rid of money and muscle power. We want to make the country's administration non-partisan.
"We hope the parties will cooperate and help develop a political culture in the country."
Political analysts say Ahmed faces an uphill task in building a consensus between the bitterly divided Awami League and the BNP, headed by two women who have not spoken to each other in nearly a decade.
|Bangladesh's election chief resigned on Sunday|
after accusation of bias [AFP]
Some have even warned that the military - believed to have nudged Iajuddin to act - could step in and take power if Ahmed's efforts fail.
Earlier on Sunday, M.A. Aziz, the chief election commissioner, said he was stepping down to help create an environment acceptable to all political parties in the run-up to elections.
Aziz went on leave in November after the opposition alliance accused him as well of bias towards the BNP, which ruled Bangladesh until the end of its term in October.
"I feel that if I continue in the post of CEC this may give certain political parties the opportunity to create once again new obstacles in the democratic process of holding national elections," Aziz said in a statement.