Alain le Roy said organising elections before August would be very difficult for logistical and technical reasons, and the prevailing security situation.
Mr Karzai has called for polls before his term ends in May. Poll authorities say it should be held by 20 August.
The president has no power to unilaterally choose election dates.
But his term of office ends on 21 May, potentially creating a constitutional crisis if polls are held much later.
According to Article 61 of Afghanistan's constitution, elections should be held 30 to 60 days before 22 May, the end of Mr Karzai's five-year term. Some observers see this announcement as a clever political manoeuvre by the president.
Mr Karzai's decision has also been criticised by the United States, which is planning to send more troops to Afghanistan, who will not arrive in time unless the election is delayed.
"Almost impossible'
Now the UN's head of peacekeeping operations, Alain le Roy, has said it would be very difficult to hold elections in April.
"We consider it .. almost impossible to get credible elections in April," said Mr Le Roy.
"At the same time, we understand there must be a consensus within the Afghans on the best constitutional way, or best way in conformity with the constitution, he added.
"We consider the debate is not closed. But our position is clear: we consider the date set was the right one."
International monitors have said it would be difficult to hold a fair election by April because of security concerns, bad weather and the logistical challenges of getting ballots.
Mr Karzai has been under considerable pressure over the delay and has been accused of using it to illegally extend his rule in breach of the constitution, says the BBC's Ian Pannell in Kabul.
Now he has put the onus for deciding when the vote should be held, and ultimately who runs the country in the event of a delay, back at the feet of the commission and his opponents, our correspondent says.
The US and other members of the international community supported the Independent Elections Commission's recommendation for an August poll, as the 17,000 foreign troops expected to bolster peacekeeping forces can be used to secure voting stations from the Taleban, reports say.
IEC chief Azizullah Ludin said that 20 August was chosen for the presidential polls after consultations with Afghan and international security forces.
"They told us there will be new security forces here... and they will guarantee security," Mr Ludin told a news conference in Kabul in January.
Afghanistan continues to experience militant attacks and suicide bombings by the Taleban, who were ousted from power in the US-led invasion of 2001.
