Karzai was giving a speech to the elders and residents of Andar district in Ghazni province when rockets were fired nearby, Ali Shah Ahmadzai, the provincial police chief, said.
No one was hurt, he said.
Witnesses said they heard between three and six rockets, but the Taliban claimed it fired off 12.
The assassination attempt was one among a spate of attacks that killed at least 66 people, mostly fighters, over the weekend in Afghanistan.
The rockets missed their target, with two of them landing some 200 metres away from the crowd, Arif Yaqoubi, a local reporter attending the event, said.
Karzai unfazed
"Please sit down," Karzai told a nervous crowd under a tent in a school yard. "Don't be scared. Nothing is happening."
Karzai finished his speech and his security detail whisked him off by helicopter to Kabul, witnesses and officials said.
It was the third attempt on Karzai's life since he became president following the ouster of the Taliban in 2001.
Qari Yousef Ahmadi, purported Taliban spokesman, said that Taliban fighters were behind the attack.
"The Taliban knew that Karzai was coming to Andar district. When Karzai was meeting with the people, the Taliban fired 12 rockets," he said by satellite phone from an undisclosed location.
"The rockets fell nearby."
Other violence
The rocket attack in Ghazni came a day after Taliban fighters attacked three separate police posts in Murghab district of Badghis province in northwestern Afghanistan.
The ensuing six-hour battle left 20 suspected Taliban members and two officers dead, General Mohammad Ayub Naizyar, the provincial police chief, said.
Police repelled the attack and sent reinforcements to the area, forcing the fighters to withdraw, he said.
Separately, in Ghazni province, one Afghan soldier was killed and four others were wounded when a roadside bomb hit their patrol on Saturday, Nato said in a statement.
British soldier dead
The toll continues to rise, meanwhile, for the Nato-led force in Afghanistan.
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British soldiers have been battling the Taliban
in Sangin in the south for months now [EPA] |
The British military said on Sunday that a Nato soldier was killed and four wounded at the weekend after a Taliban ambush near the southern Afghan town of Sangin.
Soldiers from the 1st Battalion Grenadier Guards were on patrol with Afghan troops when they were struck by a roadside bomb on Saturday, Captain Alex Corbett-Burcher, an officer with British mentoring teams who work with Afghan troops, said.
The dead soldier was later named by Britain's ministry of defence in London as Guardsman Neil "Tony" Downes, 20, from Manchester, northwest England.
Zabul fighting
Also on Saturday, Nato and Afghan troops clashed with fighters and called in air strikes, leaving 27 suspected Taliban dead in southern Zabul province, General Mohammad Zahir Azimi, defence ministry spokesman, said.
The previous day, a gun battle between combined Nato and Afghan troops and the Taliban left 16 fighters dead in Zabul, a statement from defence ministry said.
The reports could not be independently verified because the incidents occurred in remote areas.