Electricity was cut after an initial explosion at the hilltop hotel, a counterterrorism source said.
Residents in the area report a high volume of ambulances at the scene but the area has been cordoned off by security forces.
They are "shooting at guests", he said.
An Afghan spy agency official told AFP there are four militants inside the hotel.
"We are hiding in our rooms".
"Fights between insurgents and security forces are still on".
The attackers have also set fire to parts of the hotel.
Security officials said it is believed that some people have been taken hostage by the attackers.
The Department said it had received reports of "extremist groups" planning a hotel attack in the capital, "such as [on] the Hotel Baron near Hamid Karzai Int'l Airport".
There was no immediate information on casualties.
A conference on Afghanistan-China relations was held at the hotel earlier Saturday, attended by the Chinese embassy's political counsellor Zhang Zhixin.
The Intercontinental is one of two main luxury hotels in Kabul and previously came under attack in 2011.