Security officers' advance comes after at least 50 people rescued from building on Wednesday morning.
Explosions and heavy gunfire were heard Wednesday morning at about 6am (0300GMT) as security officers engaged suspected terrorists inside Grosvenor Hotel in the Dusit office complex in the Kenyan capital Nairobi.
Officers were seen advancing towards the the seventh floor of the building, said to be where the armed assailants were holed up.
Earlier at about 4am (0100GMT), at least 50 people had been rescued and reunited with their families who had camped at the road leading to the office park for more than 10 hours.
Most of those rescued were hiding on the first floor of the building under tables, chairs and in the washrooms.
According to accounts by the survivors, the security officers reached them at about 4am (0100GMT), identified themselves and escorted them out of the building.
At least four ambulances were seen leaving the compound.
Many people are still camped on Riverside Drive, the road leading to the hotel, as rescue operations continue amid gunfire.
It is feared that more people are still trapped on the seventh floor. The floor houses offices and part of the hotel.
Kenya Red Cross said that they have two official tracing hotline numbers: 0715820219 and 1199.