The attack began at about 21:00 local time (16:30 GMT), Mr Danish said. "The attackers are at one side of the building".
The same hotel had come under attack earlier in 2011 in which at least 10 people lost their lives. "I beg the security forces to rescue us as soon as possible before they reach and kill us".
Officials, however, would not confirm those reports, saying they were still gathering information. Meanwhile, deputy spokesperson Nasrat Rahimi told reporters at least for gunman had entered the hotel.
The attackers have taken several hostages in the hotel, according to local news agency Tolo News who cited Kabul police. A ministry spokesman believes the gunman used the back door of the kitchen to gain access to the hotel. "According to initial reports, no Resolute Support or (US forces) members were injured in this incident", he said in an emailed statement.More news: What's next for 13 siblings allegedly starved, held captive
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US State Department spokeswoman Heather Nauert said it was not known if any American citizens had been caught up in the attack.
The attack comes just days after the USA embassy in Kabul issued a warning about hotels in the city, saying it was aware of planned attacks by extremist groups.
Security in Kabul has been tightened since May 31 when a massive truck bomb ripped through the diplomatic quarter, killing some 150 people and wounding around 400 others- mostly civilians.
A group of insurgents stormed the Intercontinental Hotel in Bagh-e-Bala area in Kabul city at about 9.20 pm on Saturday evening. They include a bomb at a Shia cultural centre last month that killed more than 40 people.