Officials said 160 people, including 41 foreigners, were rescued from the hotel by special police forces.
Abdul Rahman Naseri, a visitor who was at the hotel for a gathering, said he was in the hall of the hotel when he saw four insurgents clothed in army outfits.
Terrified guests trapped at the top of the building tied bedsheets together and climbed over balconies to escape the overnight assault.
The Taliban has said it was behind a gun attack at a five-star hotel in the Afghan capital, in which five people were killed.
Afghan officials raised the death toll at Kabul's Intercontinental hotel to 19 Sunday as the Taliban claimed responsibility for the latest major attack on civilians in the Afghan capital.
"Our thoughts and deepest sympathies are with those affected by the terrorist attack on the Intercontinental Hotel in Kabul Afghanistan", said Elizabeth Reid, spokesperson for Global Affairs Canada, in a statement.
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Nasrat Rahimi, a deputy spokesman for the Interior Ministry, had said earlier that foreigners were among the dead, but did not provide details on the nationalities of the victims.
Several armoured USA military vehicles with heavy machine guns could be seen close to the hotel along with Afghan police units as Special Forces manoeuvred around the site.
The Intercontinental Hotel is located on a hilltop in Bagh-e Bala area of the city and is heavily guarded because it hosts both Afghan and foreign guests as well as official conferences. I tried to come down but I was heavy and my arms were not strong enough.
An official with Afghanistan's spy agency put the number of wounded at eight, while the interior ministry said six. At least 18 people were killed and hostages were seized by the Islamists in a 14-hour rampage.
After repeated strikes on Kabul, notably last May when a truck bomber killed at least 150 people outside the German embassy, security has been further tightened.
He adds the U.S.is working with Afghan authorities and is committed to supporting peace efforts.
The government of Pakistan issued a statement strongly condemning the attack, but a spokesman for the Afghan government's chief executive, Abdullah Abdullah, charged that the attack was carried out by the "Pakistan-based Haqqani Terrorist Network".
"Violence like what we witnessed yesterday has no place in Afghanistan, or anywhere else in the world", Tillerson said.