The gang reportedly also took hostages from among staff and guests, and set the building ablaze.
Interior ministry spokesman Nasrat Rahim said people had died and others had been injured but could not give details of casualty numbers.
At least two of the four attackers were killed as Afghan special forces engaged the gunmen in the hotel, it was reported.
The soldiers had cleared the first floor of the six-storey building and were searching other floors for the raiders, who appeared to have a large supply of hand grenades.
Hours after the attack began, firing appeared to ease as security forces settled in, waiting for dawn.
The militants, including at least one suicide bomber, launched the attack at about 9pm local time on Saturday, security officials said.
A witness said some foreigners were among the hotel guests but it was not clear what their nationalities were.
The hotel had been due to host an information technology conference on Sunday and more than 100 IT managers and engineers were onsite when the attack took place, Ahmad Waheed, an official at the telecommunications ministry, said.
The gunmen had entered the hotel through a kitchen door to evade heavy security at the front, local news reports said.
“We are hiding in our rooms – I beg the security forces to rescue us as soon as possible before they reach and kill us,” one guest told AFP at the start of the attack. “I can hear gunfire from somewhere near the first floor.”
Two guests at the hotel confirmed that the militants attacked when they were eating, and that people in the dining room had attempted to flee. Ahsan Ali told the Observer: “People ran to their rooms and locked themselves in – it was a dreadful scene.”
It was the latest major blow to security in the Afghan capital, which has been reeling from a string of bloody attacks by both Taliban and Isis militants.
In May last year a huge truck bomb devastated part of the diplomatic quarter, killing about 150 people and wounding about 400 others.
The most recent major attack was on 29 December, when a suicide bomber targeted a Shia cultural centre, killing more than 40 people.
No group has yet claimed responsibility for the attack on the Intercontinental, which came just two days after the US embassy put out a warning that militants might be planning to target hotels in the city.
The blaze on the top floors of the hilltop complex could be seen from across the city. Commando forces were sent in, and electricity was cut soon after the attack began, amid fears that guests had been taken hostage.
Hotel manager Ahmad Haris Nayab, who managed to escape unhurt, told Reuters people were fleeing amid bursts of gunfire on all sides.
One of the most famous buildings in Kabul, the Intercontinental was a playground for the city’s elite when it opened in 1969, with parties around the swimming pool and weddings in its halls.
It was later a base for foreign journalists during the civil war that followed the Russian withdrawal, then during the period of Taliban rule and the US-led invasion in the wake of the 9/11 attacks on America.
It has not been part of the InterContinental Hotels group since 1980, but held on to the name, which had come to mark out one of the city’s landmarks.
Refurbished a decade ago, it became popular for events and conferences, and in 2011 was targeted by the Taliban in an attack that killed 21 people.
The US has stepped up support to Afghan police and soldiers in recent months, and increased airstrikes on insurgents around the country. But security officials have warned that pressure on the battlefield could increase the danger of attacks in the capital, as insurgents attempt to prove their reach.
Isis has also been attempting to introduce sectarian violence into a war that had previously avoided at least that particular poison.
For all the civilian deaths in Kabul over four decades of civil war, until the rise of Isis very few could be chalked up to the Sunni-Shia tensions that have claimed so many lives from Iraq to Pakistan. (Courtesy The Guardian)