NATO condemned the attack and said it would make no difference to the alliance's involvement in Afghanistan.
"NATO will continue to support the Afghan Government and people in defending their security and their democracy," Secretary General Jaap de Hoop Scheffer said in a statement.
The Taliban fire appeared to come from a building a few hundred metres (yards) from the site, a road which is blocked off for official parades, close to the presidential palace.
"Three of our attackers have been killed and three managed to escape. Small arms and RPGs (rocket-propelled grenades) were used in the attack," Taliban spokesman Zabihullah Mujahid told Reuters from an undisclosed location.
The attack disproved Afghan government and NATO assertions that the Taliban insurgency has been weakened, he said.
"Afghan and NATO authorities this year repeatedly said the Taliban are on the verge of annihilation ... Now it is has been proved to them the Taliban not only have the ability to operate in the provinces, but even in Kabul," said Mujahid.
"Karzai and his cabinet can't be safe from Taliban attacks."
Immediately after the attack, bandsmen in full dress uniform and ordinary soldiers scrambled to get out of the line of fire. Other soldiers and Karzai's bodyguards, dressed in black, took up firing positions on roads near the parade ground.
Karzai has survived several assassination attempts since he came to power after U.S.-led and Afghan forces toppled the Taliban in late 2001 for failing to hand over al Qaeda leaders behind the September 11 attacks on the United States.
But Taliban insurgents regrouped and relaunched their insurgency two years ago and now fight daily battles with Afghan and foreign troops, mainly in the south and east, and have launched scores of suicide attacks throughout the country.
U.S.-led forces killed several militants on Saturday in a raid northeast of Kabul targeting a man involved in bomb attacks who was planning to disrupt ceremonies on Sunday. Several civilians were wounded in the ensuing battle in which artillery and air strikes were called in, the U.S. military said.
Karzai has repeatedly offered to hold peace talks with the Taliban, but the hardline Islamist militants have said they will fight on till they topple him and drive out the more than 50,000 foreign troops based in Afghanistan.
