Speaking on Saturday in Kabul, Karzai said the decision was "exactly what the Afghan people were hoping for" to help fight extremism and bring stability to Afghanistan.
He said it would help create "the right environment" for a peace process between the Afghan government and so-called moderate Taliban elements.
"In the right environment means ... looking at the list that is with the United Nations and removing the names that are not part of al-Qaeda, that are not part of [the] terrorist network ... and the help of the countries who have an important role in this regard must be asked for," Karzai said.
Political opponents have argued for Karzai to end his term as per the constitution and a caretaker president be appointed.
Karzai has suggested that if there were no national consensus on the issue, he would call a "Loya Jirga", or traditional gathering, to settle the matter.
Diplomats have said the presidential election is the key test of progress in Afghanistan this year.
The president, his Western supporters and opposition leaders, have all agreed that security and logistical concerns mean the polls cannot take place until August 20, the date set by the election commission.
Karzai had earlier written to the supreme court to ask for an opinion on whether he should stay in office.
Under Afghanistan's constitution, polls should be held 30 to 60 days before the end of a president's five-year term.
Afghanistan's second presidential election is seen as a key test of the country's democratic system that western powers have been seeking to have implemented following the 2001 removal from power of the Taliban in a US-led invasion.
The Nato-led International Security Assistance Force (Isaf) of nearly 62,000 soldiers, which is helping the country's government battle opposition fighters, has called on its members to deploy thousands of extra troops for the polls.
Barack Obama, the US president, unveiled a new strategy for Afghanistan and Pakistan on Friday.
He has ordered the deployment of 4,000 extra US troops to Afghanistan, on top of the 17,000 who are already on their way.
The boost will bring the number of American troops close to 60,000 at around the time of the Afghan elections.