He claimed that more than 10 US soldiers were killed and four of their military tanks were destroyed. Taliban casualty claims, however, are considered unreliable.
The attack happened hours after two rockets believed to have been fired by Taliban militants from southern Kabul landed in the fortified presidential palace.
One of the rockets hit a tree inside the palace compound, where Karzai and his family lives, while the other hit an open area near the palace, officials said. No one was hurt by the two rockets.
Kabul, which was relatively peaceful in the past six months before August, has seen an upsurge in Taliban attacks including suicide bombings and rocket attacks.
NATO-led US General Stanley McChrystal said in an interview with German media at NATO headquarters in Kabul that the city was still safer than previous years.
'Although there are isolated incidents - (Kabul) is remarkably more secure than it was even a year or two ago,' he said.
Also on Tuesday, a suicide bomber in Uruzgan's Chora district attacked a checkpoint manned by Afghan army personnel, killing three soldiers and two civilians, provincial police chief Juma Gul Hemat said.
Three more soldiers and three civilians were wounded in the blast, which took place about 30 km northeast of the provincial capital, Tarin Kowt, he said.
Thousands of Afghan and international forces are taking part in several operations in the south to flush out militants ahead of Thursday's voting.
The latest deaths brought to 276 the total number of international soldiers killed in Afghanistan so far this year. The number includes more than 150 US troops.