"People are still a little bit panicked. They are trying to stay away from fortified areas, afraid of another attack," he said.
"The Taliban spokesman said they dispatched 20 suicide bombers to Kabul and only seven of them were killed. We don't know if the other 13 are alive, or where they are."
US and Nato officials hailed local security forces for their defence of the capital.
Anne Macdonald, a US brigadier general who works closely with the Afghan interior ministry, told Al Jazeera that the Afghan national security forces "responded very well" to the attacks.
"They [security forces] were able to contain the situation within five hours," she said.
"The damage could have been much worse - to individuals and to property. They have a long way to go but they are interested and motivated. They want to serve the people of Afghanistan."
Taliban fighters staged attacks in the capital on Monday, leaving five people dead and breaching security cordons as Hamid Karzai, the Afghan president, was swearing in new members of his cabinet at the presidential palace.
Zabihullah Mujahid, the Taliban spokesman who said that 20 bombers were involved in the attacks, claimed that the intended targets were the presidential palace and the ministries around the capital's Pashtunistan Square.
One child was killed in the attacks, along with four members of the security forces.
More than 70 people were wounded after more than three hours of bombings and street battles.
Seven suspected Taliban fighters were also killed, either blowing themselves up or shot dead by the security forces.
The attack throws into question Karzai's plan to offer Taliban fighters economic incentives to put down arms and reintegrate into mainstream Afghan society.
He is due to announce a new reconciliation plan ahead of a major international conference on Afghanistan in the UK on January 28.
However, Robert Gates, the US defence secretary, said it was unlikely Taliban leaders would reconcile with Afghanistan's government, though their lower ranks - those who fight for money rather than ideology - might be open to making peace, he said.
"It's our view that, until the Taliban leadership sees a change in the momentum and begins to see that they are not going to win, that the likelihood of significant reconciliation at senior levels is not terribly great," Gates said during a flight to India.
Obama committed 30,000 extra troops to the country at the end of last year, to be focused on training local security forces, after much deliberation.