Boinnet reported that at Wednesday's press conference six new bodies were found in the complex of 14 Riverside and a policeman died due to the severity of injuries reported by local media.
Among those killed were 16 Kenyans, an Englishman, an American and three people of African descent who have not yet been identified, the inspector said.
In addition, Boinnet said 28 people were injured and that "two key suspects" were arrested in connection with the attack.
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"We have reason to believe that (the detainees) have facilitated the attack, they are helping the police in the investigation," said the police officer.
The president of Kenya, Uhuru Kenyatta, gave this Wednesday ending the police operation to reduce the assaults in the complex 14 Riverside, in the district of Westlands, where "all the terrorists were eliminated" and evacuated more than 700 people.
"My heart and that of every Kenyan is with every innocent man and woman shaken by senseless violence," lamented the head of state in a television message addressed to the nation.
The president said that "anyone involved in the planning, financing and execution of this ignominious act will be persecuted".
The Somali jihadist group Al Shabab, which joined the international network of Al Qaeda in 2012, claimed responsibility for the attack on Tuesday in a message broadcast on its Andalus radio station.
Nairobi has not suffered any jihadist jabs since September 2013, when in a similar operation on Tuesday's attack, at least four Al Shabab terrorists broke into the Westgate shopping center in Nairobi, near the 14 Riverside complex and frequented by foreigners and wealthy Kenyans.
In that attack, 67 people died during the four days when terrorists inside the building were entrenched, besieged by security forces.
The worst terrorist action suffered by Kenya was the 1998 attack on the US Embassy in Nairobi, which caused over 200 deaths and thousands of injuries.