Iajuddin, the ceremonial chief of the armed forces, also said the army he called out to reinforce security ahead of parliamentary polls on January 23 would be neutral.
''The army will act neutrally and not for any party or group,'' the president told US ambassador Patricia A Butenis, who met him at the presidential palace.
A multi-party alliance led by Sheikh Hasina, chief of the Awami League, accuses the president of being partisan towards her rival Begum Khaleda Zia, who ended her five-year term as prime minister late in October.
Iajuddin took over from Khaleda as head of an interim government charged with organising new elections within three months.
But Hasina, a former prime minister, and her allies have accused the president of bypassing the constitution in deploying the army for election duty and taking orders from Khaleda and her Bangladesh Nationalist Party (BNP).
Hasina said yesterday Iajuddin ''should step down as head of the interim authority to give the people a chance to exercise their franchise in a free and fair vote''.
''The president has failed to prove his neutrality and acted to appease (the one) who made him the president,'' she said, referring to Khaleda.
Hasina said the president ''has wasted plenty of time by sitting on lawful demands we made to make the election free''.
''The time now available for electioneering is not much,'' she told followers, without clearly asking for the vote to be postponed.
Khaleda, in separate remarks to supporters, ruled out a delay in holding the polls, saying to do so risked pushing the country into a constitutional vacuum.
''We cannot allow this,'' Khaleda added.
The two women fell out after joining forces to topple a military government in a people power movement in 1990 and have been bitter rivals since. They have not spoken to each other for a decade or more.
Hasina and her allies accuse some top officials at the Election Commission of also favouring Khaleda and the BNP in the coming polls, and want them removed immediately.
Iajuddin appointed four advisers yesterday, to replace four others who quit on Monday following differences with him over the deployment of army.
Hasina's alliance said the new advisers were ''not acceptable because they were all loyal to the president and unable to act neutrally''.
The president ordered the deployment on Saturday to assist the civil administration ahead of the polls, after 44 people were killed and hundreds injured in clashes between rival political activists in the past six weeks.
Hasina's alliance has called for a siege of election offices all over the country tomorrw.
Reuters BDP GC1939