The Kenyan Red Cross said about 50 people were unaccounted for.
"We're deeply sorry about what happened".
Ambulances and security forces were rushed to the scene, and what appeared to be plainclothes security forces were seen inching their way toward the scene.
A Kenyan police officer who was among the first responders at the at Dusit Hotel attack says he saw bodies but "no time to count the dead".
CCTV footage broadcast on local media showed four black-clad, heavily armed men entering the complex on Tuesday afternoon. He said he hid in an office.
The Interior Ministry has said that the "mopping-up process" continues but in a tweet on Wednesday morning said all buildings and the area surrounding the DusitD2 hotel complex were secure, despite renewed gunfire and explosions.
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"It's a traumatic time, it's a very stressful time ... you are wondering whether you should be messaging your loved ones to say, "Thank you, it's been swell, please forgive me and I love you", or, "Please be calm and we will be out shortly".
"I've got a good view of the High Commission from my window, and once I realised it wasn't an attack on the embassy, I realised it potentially was a more serious incident than I was anticipating", he said.
Six people were killed in an assault on a luxury hotel in Nairobi today, with Al-Shabaab claiming responsibility and the Kenyan government pleading with citizens to not spread images of the attack or "terrifying messages" on social media. The group has asserted that 47 people were killed but it gave no details in a post published by its Shahada news agency.
"We can now confirm that this criminal activity commenced at about three o'clock [1200 GMT] in a coordinated fashion and began at I&M Bank with an explosion that targeted three vehicles in the parking lot, and a suicide explosion in the foyer of Dusit hotel", he said in a statement on television.
The Shabaab targeted Kenya after it sent its army into Somalia in October 2011 to fight the jihadist group. The al-Qaida-linked group has killed hundreds of people in Kenya.
Large trails of smoke have also been seen rising from the area as scores of people have been reported injured. An unexploded grenade has been seen in a hallway of the shopping complex.
April 2015: Al-Shabab launched an assault on Garissa University College in Kenya, killing 148, mainly students. A large group of women have been hurried out by security forces, one woman still in hair curlers, another was on a stretcher. Some ducked behind cars, screaming, while others took cover behind fountains and other features at the lush complex.