An interior ministry spokesperson said the gunmen were exchanging fire with the security forces and they appeared to have included suicide bombers. The entire area has been cordoned off by the police.
They entered the hotel around 9:20 pm, local time, carrying small weapons and rocket propelled grenades or RPGs.
"They are now on the third and fourth floors fighting with our forces. We don't know the details of casualties yet but they set the kitchen on fire," interior ministry spokesman Nasrat Rahimi told AFP.
The fourth floor of the hotel is also on fire, according to an official from the National Directorate of Security.
A guest who is hiding in his room in the hotel, told AFP that he could hear gunfire. "I don't know if the attackers are inside the hotel but I can hear gunfire from somewhere near the first floor," AFP quoted the guest as saying.
This is not the first time the Intercontinental Hotel has been targeted. In June 2011, 21 people, including 10 civilians, were killed in a suicide attack.
The state-owned hotel, built in the 1960s, is not part of the global InterContinental chain. Located on a hill-top, it is heavily protected like most public buildings in Kabul, and hosts weddings, conferences and political gatherings. It is one of the two main luxury hotels in Kabul.
With inputs from AFP and Reuters
Get the latest election news, live updates and election schedule for Lok Sabha Elections 2019 on ndtv.com/elections. Like us on Facebook or follow us on Twitter and Instagram for updates from each of the 543 parliamentary seats for the 2019 Indian general elections.