The electoral commission, however, disagreed saying that staging elections in a matter of weeks was impossible given the overwhelming security problems in the insurgency-wracked central Asian country.
The United States had also voiced concerns over holding early elections.
With critics accusing the Afghan president of seeking to wrong-foot opponents by bringing forward the elections, there was speculation Karzai would announce his resignation at the news conference.
Karzai's political opponents, including several potential candidates, have called on him to hand over power to an interim administration when his term ends, particularly if he decides to stand for a second term in office.
Al Jazeera's Zeina Khodr, reporting from Kabul, said a major question remained on what will happen between May 21 - when Karzai's term of office expires - and August 20 when the election would be held.
"The president was asked that question - whether he will form an emergency government - and he ignored it. He said whoever is in power, there should be a legitimate power between May and August," she said.
"That really is the real battle; the next battle in Afghanistan."
'Playing with words'
She said that though Karzai had lost support from the West and some Afghans, he still had support as "there is no real challenger" to his rule.
"The president is playing with words. He is trying to show that he is upholding the constitution"
Daoud Sultanzoy, Afghan member of parliament
He is determined to seek re-election, she said.
Daoud Sultanzoy, an Afghan member of parliament, said it is not Karzai to "approve or disapprove" the date of the election.
"The president is playing with words. He is trying to show that he is upholding the constitution," he said.
"He is speaking from both sides of his mouth, and he is trying to show himself as a law-abiding president while he has trampled on many articles of the constitution, and we have many, many documents based on that."
He said Karzai knew what was going to happen and had he prepared the country for the election in time, "we wouldn't be facing this power vaccum after May 22".
"He wants to stay in power so that he can steal the election," Sultanzoy said.