The advisers were expected to hold a news conference later on Monday to explain their decision, TV station ATN Bangla reported.
Their move came amid media reports that they had disputed President Ahmed's deployment of the military late on Saturday to end street protests - organised by a 14-party political alliance - over electoral reforms.
In a televised speech to the nation late on Sunday, Ahmed said army had been engaged to help the civil administration to maintain law and order in the run-up to the election.
He said: "I call upon the people to extend all out co-operation to the army so that they can fulfil their task.
"I hope political parties will put the country ahead of everything and will participate in the coming election solving disputes through negotiation."
Separately, a home ministry statement on Sunday said the army was called in to aid the civil administration, and "to avert any unwarranted situation on the eve of coming general election".
Past military coups
Bangladesh, an impoverished nation of 140 million people, has been repeatedly paralysed over the past two months by the protests to demand electoral reform.
Calling in the army to help maintain law and order was viewed as a risky step in the South Asian nation, which has been plagued by military coups since gaining independence from Pakistan in 1971 - two of its presidents were slain in coups, and there have been 19 other failed coup attempts.
Past governments also have used the army for security during national elections, or in anti-crime drives and relief operations after cyclones or floods.
The Awami League-led 14-party opposition alliance will stage demonstrations across Bangladesh on Tuesday, despite the presence of the troops, Abdul Jalil, a spokesman, said on Monday.
"We plan to hold peaceful protests across the country to press for reforms that will make the upcoming polls free and fair," he said. "Our protests are not against the military but against the partisan election officials who must go."
The alliance, headed by Sheikh Hasina Wajed, a former prime minister, rejected the army deployment as an effort to intimidate the group's supporters.
The alliance wants the removal of two election commissioners who it accuses if bias towards Khaleda Zia, the former prime minister and an arch-rival of Hasina.
Under Bangladesh's constitution, election officials cannot be sacked, but must resign or go on leave.
No further delay
A top election official meanwhile said the advisers' resignations would not further delay the polls, scheduled for January 23.
"Definitely, the elections will be held on time," Mahfuzur Rahman, the acting chief election commissioner, said on Monday.
Meanwhile, soldiers patrolled Bangladesh's towns and cities for a second day after the president called out the military late on Saturday.
More than 17,000 army, navy and air force troops were deployed in towns and cities to "assist the civil administration in maintaining law and order" across the country, Lieutenant-Colonel Anisur Rahman, military spokesman, said on Monday.
He said the troops may be sent to villages, "if the situation demands".
Police indefinitely banned public gatherings or protests around the presidential palace, and armoured vehicles have taken up positions around the colonial-era building. The alliance cancelled plans on Sunday to march on the palace.